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8.06 Modeling with right triangles

Adaptive
Worksheet

Interactive practice questions

A man standing at point $C$C, is looking at the top of a tree at point $A$A. Identify the angle of elevation in the figure given.

A right triangle is shown with vertices labeled A, B and C. Side AB is the vertical leg, side BC is the horizontal leg, and side AC is the hypotenuse. The right angle is at vertex B, as indicated by a small square. There are two arcs indicating angles: one at vertex C, labeled with $\alpha$α, and another at vertex A, labeled with $\theta$θ. Above vertex C, a vertical dotted line extends from vertex C to a point labeled D. The angle between this dotted line CD and the hypotenuse AC is labeled with $\sigma$σ.

$\alpha$α

A

$\theta$θ

B

$\sigma$σ

C
Easy
< 1min

A man standing at the top of the tower at point $B$B, is looking at the ground at point $C$C. Identify the angle of depression in the figure given.

Easy
< 1min

Considering the diagram below, find $x$x, the angle of elevation to point $A$A from point $C$C.

Round your answer to two decimal places.

Easy
2min

Sally measures the angle of elevation to the top of a tree from a point $20$20m away to be $43^\circ$43°. If the height of the tree is $h$h m, find the value of $h$h.

Round your answer to the nearest whole number.

Easy
1min
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Outcomes

G.N.Q.A.1

Use units as a way to understand real-world problems.*

G.N.Q.A.1.B

Define and justify appropriate quantities within a context for the purpose of modeling.

G.SRT.C.5

Solve triangles.*

G.SRT.C.5.A

Know and use the Pythagorean Theorem and trigonometric ratios (sine, cosine, tangent, and their inverses) to solve right triangles in a real-world context.

G.SRT.C.5.B

Know and use relationships within special right triangles to solve problems in a real-world context.

G.MP1

Make sense of problems and persevere in solving them.

G.MP2

Reason abstractly and quantitatively.

G.MP3

Construct viable arguments and critique the reasoning of others.

G.MP4

Model with mathematics.

G.MP5

Use appropriate tools strategically.

G.MP6

Attend to precision.

G.MP7

Look for and make use of structure.

G.MP8

Look for and express regularity in repeated reasoning.

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