1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mote1985 [20]
1 year ago
15

How to use trig to find missing side or angle of right triangles.

Mathematics
1 answer:
andrew11 [14]1 year ago
8 0
Explanation

Right triangles are triangles with one right angle i.e. one angle with a measure of 90° so when we deal with this type of figures we know at least one of its internal angles. The opposite side to the right angle is known as the hypotenuse whereas the other two sides are called legs.

Trigonometric functions in right triangles give us the following identities:

\begin{gathered} \tan x=\frac{\text{opposite side}}{\text{adjacent side}} \\ \cos x=\frac{\text{adjacent side}}{\text{hypotenuse}} \\ \sin x=\frac{\text{opposite side}}{\text{hypotenuse}} \end{gathered}

We also have the Pythagorean theorem that states that the square of the hypotenuse is the sum of the squares of the legs.

Let's imagine that we have a right triangle like the following:

If we want to find the missing angles A and/or B we need to know at least two sides of the triangle.

For example, if we want to find B and we have b and a we can use the tangent of B and its inverse the arctangent (tan^(-1)):

\tan B=\frac{b}{a}\rightarrow B=\tan^{-1}(\frac{b}{a})

If we know a and c we can find B using its cosine:

\cos B=\frac{a}{c}\rightarrow B=\cos^{-1}(\frac{a}{c})

If we know b and c then we can use the sine:

\sin B=\frac{b}{c}\rightarrow B=\sin^{-1}(\frac{b}{c})

We can also do the same for angle A, we just need to use its corresponding opposite side and adjacent side. And that's how you find a missing angle using trigonometry in a right triangle.

If we are looking for a missing side we can also use trigonometry. In order to find a missing side we need two other sides or another side and an angle. For example, let's assume that we want to find side a.

If we have b and c then we just need to use the Pythagorean theorem:

c^2=a^2+b^2\rightarrow a=\sqrt{c^2-b^2}

If we have b and A then we can use the tangent of A to built an equation for a:

\tan A=\frac{a}{b}\rightarrow a=b\cdot\tan A

If we have b and B we can use the tangent of B:

\tan B=\frac{b}{a}\rightarrow a=\frac{b}{\tan B}

If we have A and c we can use the sine of A:

\sin A=\frac{a}{c}\rightarrow a=c\cdot\sin A

If we have B and c we can use the cosine of B:

\cos B=\frac{a}{c}\rightarrow a=c\cdot\cos B

And that's how you find a missing side using trigonometry.

You might be interested in
Does this graph represent a function?
kupik [55]
Yes and the correct one is A
5 0
3 years ago
Tanner earns $14.50 per hour for the first 8 hours he works each day. For every hour worked over 8, he earns 1.75 of his normal
bogdanovich [222]

Answer:

167.19

14.50 x 8 = 116.00

14.50 + 1.75 = 16.25 per hour overtime

16.25 × 3.15 hour overtime = 51.19

116.00 + 51.19 = 167.19

Step-by-step explanation:

7 0
3 years ago
Use the intersect method to solve the equation x^2-1=-x^2+7
olga55 [171]

Answer:

The solutions of the equation x^2-1=-x^2+7 are (-2,3) and (2,3)

Step-by-step explanation:

Please, see the attached file.

Thanks.

4 0
3 years ago
Tim is 35 years old. He is 7 years younger than 6 times his daughter's age. The equation,
Oksana_A [137]

Answer:

A. 7 years old

Step-by-step explanation:

6x-7=35 is the equation.

Add 7 to both sides, which gives you 6x=42.

Then both sides by 6, so 6/6=x and 42/6=7

So, x=7.

Since x is his daughter's age, x=7, so his daughter is 7.

6 0
2 years ago
Read 2 more answers
What is 14100/3.6 as a whole number
malfutka [58]

Answer:

3916.6

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • You and a friend both would like a salad and a small drink. Between the two of you you have $8.00. A salad costs $2.49 and a sma
    6·1 answer
  • (4x2 + 7x - 4) + (x2 - 7x + 14)
    7·1 answer
  • Which ratio best defines experimental probability?
    15·2 answers
  • Find Surface Area...
    7·1 answer
  • What is the gcf of 5 (4x-3) +x (4x-3)? Explain
    6·1 answer
  • Simplify (4/5) (5/6) (6/7) (7/8) (8/9)
    8·2 answers
  • Help me please !!!!!!
    13·1 answer
  • The function g(x) is a transformation of the cube root parent function,
    13·1 answer
  • Equations
    10·1 answer
  • Simplify the expression.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!