Lesson 10
Solving Problems with Trigonometry
- Let’s solve problems about right triangles.
Problem 1
Technology required. Find the area of the isosceles trapezoid.
Problem 2
Technology required. The sun is 62 degrees above the horizon. A tree casts a shadow that is 12 feet long. How tall is the tree?
Problem 3
Technology required. A plane leaves the ground with an elevation angle of 6 degrees. The plane travels 10 miles horizontally.
- How high is the plane at the time?
- What is the distance of the plane’s path?
Problem 4
Technology required. Find the missing measurements.
Problem 5
Technology required. Ramps in a parking garage need to be both steep and safe. The maximum safe incline for a ramp is 8.5 degrees.
Is this a safe ramp? Explain or show your reasoning.
![Right triangle. Base 100 units, height 20 units. A car is drawn above the hypotenuse.](https://staging-cms-im.s3.amazonaws.com/kJ92UwG4ZnJ8yPKqZhfxHPgA?response-content-disposition=inline%3B%20filename%3D%22download.png%22%3B%20filename%2A%3DUTF-8%27%27download.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T072915Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8fa079a49e418f4e4e7b1a6acda18983199a05ddf0273f80f37d0200a8cc343c)
Problem 6
Select all true equations.
\(\cos(37)=\sin(53)\)
\(\tan(37)=\tan(53)\)
\(\sin(37)=\cos(53)\)
\(\sin(37)=\sin(53)\)
\(\cos(\theta)=\sin(90-\theta)\)
Problem 7
Technology required. Clare is flying a kite. She gets tired, so she stakes the kite into the ground. The kite is on a string that is 30 ft long and makes a 27 degree angle with the ground. How high is the kite?
30 ft
13.6 ft
26.7 ft
15.3 ft
Problem 8
What is the length of the diagonal?