a building casts a 25 foot shadow on a sunny day. If the angle of elevation from the tip of the shadow to the top of the building is 65 degrees, what is the height of the building to the nearest tenth of a foot?
I did tan =x/25
x=25tan65
x=53.61267301
x=53.6 feet
the height of the building is 53.6 ft tall.
Is this correct?
thanks
tan 65 = h/25
yes
Your calculation is partially correct, but there is a small mistake in your calculation.
To find the height of the building, you need to use the trigonometric function tangent (tan) to find the ratio of the height to the length of the shadow. Here's the correct calculation:
tan(angle) = height / length of shadow
tan(65 degrees) = height / 25 feet
To find the height, you can rearrange the equation:
height = tan(65 degrees) * 25 feet
Now, let's calculate it:
height = tan(65 degrees) * 25 feet
height ≈ 1.88072646515 * 25 feet
height ≈ 47.0181616288 feet
So, the height of the building, rounded to the nearest tenth of a foot, is approximately 47.0 feet.