# Lesson 10 Using Trigonometric Relationships Practice Understanding

Based on each set of similar triangles or parallel lines, create a proportion and solve it to find the missing values.

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Solve each right triangle. Give any missing sides and missing angles.

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Use trigonometric ratios and the Pythagorean theorem to solve each problem.

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Jack is looking up the hill at Jill and wondering how much vertical increase there actually is from his position to her position on the hill. They know there is a

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Kim is trying to use the shadow of a large tree to measure the height of the tree. The length of the shadow has been measured as

Model each of the situations with a right triangle and then solve the triangle to find the desired values.

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Alex is standing on the top of a building looking out at a boat in the lake. The distance from the top of the building to the ground is

Solution:

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The altitude of a plane is

Solution:

Use the given trigonometric ratio, which is based on actual side length measures, to sketch a right triangle and solve the triangle.

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Solution:

Sketch:

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Solution:

Sketch:

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Solution:

Sketch:

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Solution:

Sketch:

Sketch a drawing of the situation, then solve each problem.

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Mark is building his son a pitcher’s mound so he can practice for his upcoming baseball season in the backyard. Mark knows the league requires an incline of

Solution:

Sketch:

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Susan is designing a wheelchair ramp. Wheelchair ramps require a slope that is no more than

Solution:

Sketch:

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Michael is designing a house with a roof pitch of

Solution:

Sketch: