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lbvjy [14]
3 years ago
11

Alex is trying too find the height of a triangular wall. He already knows the area and the base measurement of the wall . What i

s the equation for the area of a triangle written in terms of the height?
Mathematics
1 answer:
Andrei [34K]3 years ago
8 0
The area of a triangle is A= \frac{1}{2} bh. solving for h (height) we get:
h= \frac{2A}{b}
You might be interested in
If c= 205 angle A=81 and angle B=50. b=
zlopas [31]

Answer:

Solution to Problem 1:

Use the fact that the sum of all three angles of a triangle is equal to 180 o to write an equation in C.

A + B + C = 180 o

Solve for C.

C = 180 o - (A + B) = 43 o

Use sine law to write an equation in b.

a / sin(A) = b / sin(B)

Solve for b.

b = a sin (B) / sin(A) = (approximately) 5.4 cm

Use the sine law to write an equation in c.

a / sin(A) = c / sin(C)

Solve for c.

c = a sin (C) / sin(A) = (approximately) 7.1 cm

Problem 2

The angle of elevation to the top C of a building from two points A and B on level ground are 50 degrees and 60 degrees respectively. The distance between points A and B is 30 meters. Points A, B and C are in the same vertical plane. Find the height h of the building(round your answer to the nearest unit).

diagram problem 2

Solution to Problem 2:

We consider triangle ABC. Angle B internal to triangle ABC is equal to

B = 180 o - 60 o = 120 o

In the same triangle, angle C is given by.

C = 180 o - (50 o + 120 o) = 10 o

Use sine law to find d.

d / sin(50) = 30 / sin(10)

Solve for d.

d = 30 *sin(50) / sin(10)

We now consider the right triangle.

sin (60) = h / d

Solve for h.

h = d * sin(60)

Substitute d by the expression found above.

h = 30 *sin(50) * sin(60) / sin(10)

Use calculator to approximate h.

h = (approximately) 115 meters.

Problem 3

A triangle ABC has side a = 12 cm, side b = 19 cm and angle A = 80 o (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).

Solution to Problem 3:

Use sine law to write an equation in sin(B).

a / sin(A) = b / sin(B)

Solve for sin(B).

sin (B) = (b / a) sin(A) = (19/12) sin(80) = (approximately) 1.6

No real angle B satisfies the equation

sin (B) = 1.6

The given problem has no solution.

Problem 4

A triangle ABC has side a = 14 cm, side b = 19 cm and angle A = 32 o (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).

Solution to Problem 4

Use sine law to write an equation in sin(B).

a / sin(A) = b / sin(B)

Solve for sin(B).

sin (B) = (b / a) sin(A) = (19/14) sin(32) = (approximately) 0.7192

Two angles satisfy the equation sin (B) = 0.7192 and the given problem has two solutions

B1 = 46.0 o and B2 = 134 o

Solution 1: Find angle C1 corresponding to B1

C1 = 180 - B1 - A = 102 o

Solution 1: Find side c1 corresponding to C1

c1 / sin(C1) = a / sin(A)

c1 = 14 sin(102) / sin(32) = (approximately) 25.8 cm

Solution 2: Find angle C2 corresponding to B2

C2 = 180 - B2 - A = 14 o

Solution 2: Find side c2 corresponding to C2

c2 / sin(C2) = a / sin(A)

c1 = 14 sin(14) / sin(32) = (approximately) 6.4 cm

Exercises

1. A triangle ABC has angle A = 104 o, angle C = 33 o and side c = 9 m. Solve the triangle ABC by finding angle B and sides a and b.(round answers to 1 decimal place).

2. Redo problem 2 with the distance between points A and B equal to 50 meters.

Solutions to Above Exercises

1. B = 43 o, a = 16.0 m , b = 11.3 m

2. 191 meters.

More References and Links to Sine and Cosine Laws

sine law

Sine Law Calculator and Solver.

Geometry Tutorials, Problems and Interactive Applets.

Cosine Law Problems.

Cosine Law Calculator and Solver.

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Sine Law Calculator and Solver

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Sine Law - Ambiguous case - applet

Triangles

Triangle Problems

7 0
3 years ago
How much is 1/4 of 1/3 of a chocolate cake
hoa [83]

1/3 ÷1/4 = 1/3 × 1/4 = 1/12

7 0
3 years ago
At a competition with 7 runners, medals are awarded for first, second, and
il63 [147K]

Answer:

Option A - Permutation; number of ways = 210

Step-by-step explanation:

Given : At a competition with 7 runners, medals are awarded for first, second, and  third places. Each of the 3 medals is different.

To find : How many ways are there to  award the medals?        

Solution :

There are 7 runners but medals are three.

The first runner up got first medal as one is locked.

The second runner up got second medal as second is locked.

The third runner up got the third medal.

So, There is a permutation.

Number of ways to award the medals is ^7P_3

We know, ^nP_r=\frac{n!}{(n-r)!}

Substitute the values,

^7P_3=\frac{7!}{(7-3)!}

^7P_3=\frac{7\times 6\times 5\times 4!}{4!}

^7P_3=210

Therefore, Option A is correct.

Permutation; number of ways = 210

6 0
3 years ago
Find the​ mean, variance, and standard deviation of the binomial distribution with the given values of n and p. ​, The​ mean, ​,
klemol [59]

Complete Question

Find the​ mean, variance, and standard deviation of the binomial distribution with the given values of n and p. ​, The​ mean, ​, is nothing. ​(Round to the nearest tenth as​ needed.)

    p =  0.6   n =  18

Answer:

The mean   \mu  = 10.5

The standard deviation \sigma =  2.08

The  variance   var  = 4.32

Step-by-step explanation:

From the question we are told that

      The probability of success   is  p = 0.6

      The  sample size is n = 18

  Generally given that the distribution is binomial, then the probability of failure is mathematically represented as

              q =  1- p

substituting values

              q =  1-  0.6

              q =0.4

Generally the mean is mathematically evaluated as

             \mu  =  np

substituting values

             \mu  =  18 * 0.6    

             \mu  = 10.5

The  standard deviation is evaluated as

              \sigma =  \sqrt{npq}

substituting values

               \sigma =  \sqrt{18 *  0.6 * 0.4}

              \sigma =  2.08

The variance is evaluated as

               var  =  \sigma^2

substituting value

              var  = 2.08^2

              var  = 4.32

4 0
4 years ago
AH the second question
Degger [83]

Answer:

ii. 55 degrees.

Step-by-step explanation:

(ii)

Consider the  quadrilateral ABCD.

Angle n = 180 - 96 = 84 degrees  ( opposite angles of a cyclic quadrilateral are supplementary).

Consider triangle ABC: the 3 angles are supplementary, so

m < j = 180 - 84 - 41

=  55 degrees.

4 0
3 years ago
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