On the way to the office, Susan was told that when she stands 123 ft from the base of the building, the angle of elevation of its top is 26°30°. If her eyes are 5 ft above the ground, find the height of the building.
What is 123*tanAngle + 5ft
67
To find the height of the building, we can use basic trigonometry.
Let's represent the height of the building as "h".
From the given information, we know that Susan's eyes are 5 ft above the ground, and the angle of elevation to the top of the building is 26°30°.
Using the tangent function, we can set up the following equation:
tan(26°30°) = h / (123 + 5)
First, let's convert the angle from degrees to radians:
26°30° = 26 + (30/60) = 26.5°
Now, let's convert the angle from degrees to radians:
26.5° = 26.5 * (π/180) ≈ 0.46365 radians
Now, substitute the values into the equation:
tan(0.46365) = h / 128
Using a calculator, we find that the tangent of 0.46365 is approximately 0.4787.
0.4787 = h / 128
To solve for "h", we multiply both sides of the equation by 128:
0.4787 * 128 = h
61.31 ft ≈ h
Therefore, the height of the building is approximately 61.31 ft.
To find the height of the building, we can use the trigonometric concept of tangent.
1. First, let's draw a diagram to visualize the situation described. The building forms a right triangle with the ground.
|
|
H |\
| \ <-- angle of elevation = 26°30'
| \
|------\
D 123 ft
H - Height of the building (what we want to find)
D - Distance from Susan to the building's base (123 ft)
O - Eyes height above the ground (5 ft)
θ - Angle of elevation (26°30')
2. We can see that the tangent of the angle of elevation (θ) is equal to the ratio of the height of the building (H) to the distance (D) from Susan to the building's base.
tan(θ) = H/D
3. Rearranging the equation, we have:
H = tan(θ) * D
4. Substitute the given values:
Distance D = 123 ft
Angle of elevation θ = 26°30'
H = tan(26°30') * 123 ft
5. Now, we can evaluate the tangent of 26°30'. If you are using a scientific calculator or an online calculator, make sure it is set to degree mode.
tan(26°30') ≈ 0.502414086
6. Finally, multiply the result from step 5 by the distance D:
H ≈ 0.502414086 * 123 ft
H ≈ 61.78 ft
Therefore, the height of the building is approximately 61.78 ft.