the angles of elevation of the top of a house from the bottom of a tower 160m high is 26° from the top of a tower the angle of elevation is 24°. what is the height of the house if the tower and the house are 50m apart?
I don't understand, please show the solution. Thanks
from the top of the tower you do not look UP to the house. Do you have the sign wrong or the word wrong or what?
182.3m
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Am still learning
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That's why am solving so as to know
To solve this problem, we can use the concept of trigonometry, specifically the tangent function. Here's how to find the height of the house:
Step 1: Draw a diagram to visualize the situation. Label the tower as "T", the house as "H", the distance between them as "50m", and the height of the tower as "160m".
Step 2: Identify the angles of elevation and the sides of the triangle involved. The angle of elevation from the bottom of the tower to the top of the house is 26°, and the angle of elevation from the top of the tower to the top of the house is 24°. The height of the tower is given as 160m, and the distance between the tower and the house is 50m.
Step 3: Set up two right triangles, one for each angle of elevation. In the first triangle, the side opposite the angle of 26° is the height of the house (H), and the adjacent side is the distance between the tower and the house (50m). In the second triangle, the side opposite the angle of 24° is the height of the tower (160m + H), and the adjacent side is the same as the first triangle (50m).
Step 4: Apply the tangent function to both triangles. The tangent of an angle is equal to the ratio of the side opposite the angle to the side adjacent to it. In the first triangle, we have tan(26°) = H / 50m. In the second triangle, we have tan(24°) = (160m + H) / 50m.
Step 5: Solve the equations for H. Rearrange the equation from the first triangle to H = tan(26°) * 50m. Substitute this value into the second equation to get tan(24°) = (160m + tan(26°) * 50m) / 50m. Simplify this equation to find the value of H.
Step 6: Use a calculator to evaluate the trigonometric functions and solve for H. The approximate value of the height of the house is H = 149.17m.
Therefore, the height of the house is approximately 149.17 meters.
Tan26/1=opp/adj=he/x
he=xtan26=tan24=he/50
he=50tan24
=50xo.445=22.25
height 0f the house=h+he
=160+22.25
=182.25