8-5 Angles of Elevation and Depression. You used similar triangles to measure distances indirectly. . Solve problems involving angles of elevation and depression. Use angles of elevation and depression to find the distance between two objects. Vocabulary.
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You used similar triangles to measure distances indirectly.
Angle of elevation – the angle formed by a horizontal line and an observer’s line of sight to an object above the horizontal line.
Angle of depression – the angle formed by a horizontal line and an observer’s line of sight to an object below the horizontal line
Make a drawing.
Since QR is 25 feet and RS is 5 feet 6 inches or 5.5 feet, QS is 30.5 feet. Let x represent PQ.
Multiply both sides by x.
Answer:The audience member is about 60 feet from the base of the platform.
DISTANCE Maria is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water and the angle of depression is 52°, what is the horizontal distance from the seal to the cliff, to the nearest foot?
Make a sketch of the situation.
Let x represent the horizontal distance from the seal to the cliff, DC.
C = 52°; AD = 40, and DC= x
Multiply each side by x.
Divide each side by tan 52°.
A. 19 ft
B. 20 ft
C. 44 ft
D. 58 ft
Understand ΔMLK andΔMLJare right triangles. The distance between the dolphins isJK or JL – KL. Use the right triangles to find these two lengths.
Divide each side by tan
Multiply each side by JL.
Use a calculator.
Multiply each side by KL.
Use a calculator.
Answer:The distance between the dolphins is JK – KL. JL – KL≈ 219.93 – 211.96, or about 8 meters.
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