9.6 Solving Right TrianglesUnit IIC Day 6

Do NowFill in the ratios with words.

sin(θ) =

cos(θ) =

tan(θ) =

Solving a right triangleEvery right triangle has one right angle and two

_________ angles.

Every right triangle has one _____________ and two __________.

To solve a right triangle means to determine the measures of all ______ parts. You can solve a right triangle if given one of the following situations:Two side lengthsOne side length and one acute angle measure

Inverse FunctionsThe inverse of a function switches its inputs

and outputs.Example: For f(x) = x2, if you input 3, the output is

9. Its inverse is f(x) = √x: If you input 9, the output is 3.

tan(θ) takes ___________ as its input and gives ________________ as its output,

Its inverse, tan– 1(x), takes _______________ as its input and gives _____________ as its output.

Example: sin(30º) = ___, so sin-1(___) = ____

Example 1:Solve the right triangle. Round the

decimals to the nearest tenth.

Ex. 2: Solving a Right TriangleSolve the right triangle. Round

decimals to the nearest tenth.

Ex: 3: Real Lifea) When the shuttle’s

altitude is about 15.7 miles, its horizontal distance to the runway is about 59 miles. What is its glide angle? Round your answer to the nearest tenth.

Ex: 3: Real Lifeb) When the space

shuttle is 5 miles from the runway, its glide angle is about 19°. Find the shuttle’s altitude at this point in its descent. Round your answer to the nearest tenth.

ClosureWhat is the minimum amount of information you

need to solve a right triangle?