# PreCalculus Final (Final example)

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Last updated 5 years ago

Discipline:
Math
Subject:
Pre-Calculus
11   Example 3: Solving a Right Triangle

SOLVE PROBLEM

A right triangle with the hypotenuse of 8 inches includes a 37° angle. Find the measures of the other two angles and the lengths of the other two sides.

1. We have one side and two angles.We have to solve the two missing sides and one angle.

8

y

Even though the problem says we have one side, we are already given another angle because its a Right Triangle.

37°

So how do you find the other angle?

We already have two angles, what can we do with them?

___

2a. Since we are given the hypotenuse, we can find Sine. Why? Because the side we are trying to find is the opposite. We can not use cosine because of the angle we are starting with.

53

-

90

37

x

2. Now that we have another angle, we can work on finding the other sides.

Subtract!

37°

y

8

X

53°

8

Sin 37°=

3. Okay, so now we have two sides and two ways to find the last side.

a. Pythorgean Theroem

*

_

Sin 37°=

8

_

8

x

8

*

*

8

x

8

_

8

Sin 37°=

*

x

37°

8

Sin 37°=

cos 37°=

Note: you can put this into your calculator, but it HAS to be in degree mode and round to two decimal places

b. solving it with cosine

x=

4.81

6.39

8

53°

4.81

x

y

_

8

8

_

y

cos 37°=

8

8

*

*

*

*

8

8

cos 37°=

_

8

y

y

cos 37°=

8

y= 6.39