6.3 Use Trigonometry to Find an Angle

The __________________ of trigonometric functions will calculate size of the acute _____________in a right triangle. 𝜃, __________ indicates the acute angle. The __________________ and _____________________ are given. What trig ratio relates the given sides to the angle, 𝜃?

Set up an equation: Take the inverse of each side:

The __________________ and _____________________ are given.

𝜃

What trig ratio relates the given sides to the angle, 𝜃?

13

12 Set up an equation: Take the inverse of each side:

_______________________ is equivalent to __________________________.

In general…

_______________________ is equivalent to __________________________. _______________________ is equivalent to __________________________. Use your calculator to determine 𝜃 to the nearest hundredth of a degree. 2

1

1

1) sin 𝜃 = 3

2) tan−1 2 = 𝜃

3) arccos 2 = 𝜃

4) 𝜃 = sin−1 2

5) tan 𝜃 = 0.3791

6)cos −1 0.3214 = 𝜃

7)tan 𝜃 = 1.5

8) arcsin (.0258) = 𝜃

While hiking, you see an interesting rock formation on the side of a vertical cliff. You stand on the path at a certain place, 50 feet from the base of the cliff, the rock formation is visible about 30 feet up the cliff. At what angle are you looking?   

Draw and label a picture. Determine which trig function is needed. Set up and solve an equation.

You are at a hot air balloon festival. You are 200 feet away from one particular balloon when it begins its ascent. Draw a diagram.

Let 𝜃 represent the angle formed by the balloon, you, and the lift-off point. Determine the value of 𝜃 when the balloon is 200 feet in the air.

When the balloon begins its ascent, it is 400 feet away from you, what is the value of 𝜃?