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3 years ago

The hypotenuse of a right triangle is 50 and the short leg is 30, find the projection of the leg onto the hypotenuse

Mathematics

1 answer:

gladu [14]3 years ago

6 0

Consider the attached figure. All the triangles shown are similar, so

CB/CA = CD/CB
30/50 = projection/30
projection = 30^2/50
projection = 18

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Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC . FIRST CORRECT ANSWER GETS POINTS AND BRAINLIEST!!!! T

Ad libitum [116K]

Answer:

Given : In △ABC, m∠A=60°, m∠C=45°,and AB=8 unit

Firstly, find the angles B

Sum of measures of the three angles of any triangle equal to the straight angle, and also expressed as 180 degree

∴m∠A+ m∠B+m∠C=180 ......[1]

Substitute the values of m∠A=60° and m∠C=45° in [1]

$60^{\circ}+ m\angle B+45^{\circ}=180^{\circ}$

$105^{\circ}+ m\angle B=180^{\circ}$

Simplify:

$m\angle B=75^{\circ}$

Now, find the sides of BC

For this, we can use law of sines,

Law of sine rule is an equation relating the lengths of the sides of a triangle to the sines of its angles.

$\frac{\sin A}{BC} = \frac{\sin C}{AB}$

Substitute the values of ∠A=60°, ∠C=45°,and AB=8 unit to find BC.

$\frac{\sin 60^{\circ}}{BC} =\frac{\sin 45^{\circ}}{8}$

then,

$BC = 8 \cdot \frac{\sin 60^{\circ}}{\sin 45^{\circ}}$

$BC=8 \cdot \frac{0.866025405}{0.707106781} =9.798$ unit

Similarly for AC:

$\frac{\sin B}{AC} = \frac{\sin C}{AB}$

Substitute the values of ∠B=75°, ∠C=45°,and AB=8 unit to find AC.

$\frac{\sin 75^{\circ}}{AC} =\frac{\sin 45^{\circ}}{8}$

then,

$AC = 8 \cdot \frac{\sin 75^{\circ}}{\sin 45^{\circ}}$

$AC=8 \cdot \frac{0.96592582628}{0.707106781} =10.9283$ unit

To find the perimeter of triangle ABC;

Perimeter = Sum of the sides of a triangle

i,e

Perimeter of △ABC = AB+BC+AC = 8 +9.798+10.9283 = 28.726 unit.

To find the area(A) of triangle ABC ;

Use the formula:

$A = \frac{1}{2} \times AB \times AC \times \sin A$

Substitute the values in above formula to get area;

$A=\frac{1}{2} \times 8 \times 10.9283 \times \sin 60^{\circ}$

$A = 4 \times 10.9283 \times 0.86602540378$

Simplify:

Area of triangle ABC = 37.856 (approx) square unit

4 0

3 years ago

The answer . What is the equation and the answer ?

Ksenya-84 [330]

The answer is a 8 days. the equation say's at the beginning of the day he read's 50 page's and later read's 14. this is everyday so. add 50+14+64. divide 400 by 64 and you get 7.8125, round that up and you get 8<span />

4 0

3 years ago

A conjecture and the flowchart proof used to prove the conjecture are shown.

dexar [7]

Okay. An obtuse triangle is any triangle that has 1 angle that measures more than 90°. As we can see, angle QRS measures 76° and angle PRQ measures 104°. 104 > 90. Triangle PQR is a closed figure, and a triangle measures 180° total. There can only be 1 obtuse angle in any triangle. PRQ is an obtuse angle. Therefore, triangle PQR is an obtuse triangle.

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3 years ago

Read 2 more answers

. An average car uses 1 ounces of

Inessa [10]

ANSWER:

2 ounces.

EXPLANATION:

it uses 1 once of gasoline every time it is on not driving and it is at a traffic light for 2 minutes then 1 + 1 = 2.

1 ounce + 1 ounce = 2 ounces of gasoline it uses.

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2 years ago

Two cars left the city for a suburb, 480 km away, at the same time. The speed of one of the cars was 20 km/hour greater than the

Alex_Xolod [135]

The speed of both the cars are 80km/h and 60km/h

<u>Step-by-step explanation:</u>

Let the speed of one car be 'a' and the speed of other car be 'b'.

The total distance (d) = 480km

It is given that the speed of one car is 20km/h faster than the other.

We can write,

a = b+20

The slower car takes 2 hrs more to reach the suburb than the other car.

Let the time taken by the fastest car be t

Speed = distance/time

So,

a = 480/ t

b = 480/(t+2)

We got the values of a and b.

a = b+20

480/t = (480/(t+2)) + 20

Taking LCM on the right side.

480/t = (480 + 20t + 40) / (t+2)

480(t+2) = (480+20t+40) t

480t + 960 = 480t + 20t(t) + 40t

20t(t) + 40t - 960 = 0

Divide the whole equation by 20 to simplify the equation.

t(t) + 2t - 48 = 0

Solve the quadratic equation by splitting the middle terms.

t(t) + 8t - 6t - 48 = 0

t(t + 8) - 6(t + 8) = 0

(t- 6) (t+8) =0

t = 6 (or) -8

t is time and cannot be negative. So t= 6hrs

a = 480/t

a = 480/ 6 = 80

the speed of the fastest car is 80km/hr

a = b + 20

b = a - 20

b = 80 - 20

b = 60km/h

4 0

3 years ago