A rock climber looks at the top of a vertical rock wall at an angle of elevation of 74 degrees. He is standing 4.2m from the base of the wall and his eyes are 1.5m from the ground. How high is the wall, to the nearest tenth of a meter?
o_o I'm clueless
clueless? check the topic of this section of your text.
Review the definition of tan(x).
Draw a diagram.
Then it is clear that the height is given by
1.5 + 4.2 tan 74°
No worries, I'm here to help! We can solve this problem using trigonometry. Specifically, we can use the tangent function to find the height of the wall.
First, let's draw a diagram to visualize the problem.
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| /|
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h | / |
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|/ |
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In the diagram, the line h represents the height of the wall, the vertical line represents the ground, and the angle of elevation is labeled as 74 degrees.
Given that the rock climber is standing 4.2m from the base of the wall and his eyes are 1.5m from the ground, we can determine the total height he sees by adding these two distances: 4.2m + 1.5m = 5.7m.
Now, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height h, and the adjacent side is the distance from the base of the wall to the climber (4.2m). So we have:
tan(74 degrees) = h / 4.2
To solve for h, we can rearrange the equation:
h = tan(74 degrees) * 4.2
Using a calculator, we find that tan(74 degrees) is approximately 3.076, so:
h = 3.076 * 4.2
= 12.9112
Rounding to the nearest tenth, the height of the wall is approximately 12.9 meters.
Therefore, the wall is approximately 12.9 meters high. I hope this helps!