Question

A ramp into a building forms an 8° angle with the ground. If the entry point of the ramp is 7 feet from the building, how many feet from the ground is the end of the ramp? Round the solution to the nearest hundredth.

0.98 feet
1.22 feet
1.36 feet
2.01 feet

Answer 1

Answer:

0.98

Step-by-step explanation:

First, you are trying to find the cosecant of 8, so you would set up your equation as csc8= x/7. Afterwards multiply 7 on each side of the equation, giving you 7 x csc8 = x. csc8 is equal to 0.139173101. Multiplying that by 7 gives you the rounded answer of 0.98.

Answer 2

The distance between the ground and the end of the ramp is 0.98 feet.

What is the tangent of an angle?

The tangent of an angle is the ratio of the opposite side and the adjacent side of that angle in the right-angle triangle.

tan θ= opposite side/ adjacent side

Here in the picture, AB is the height of the building and AC is the length of the ramp.

Given that the ramp forms 8° with the ground.

∠ACB= 8°

Given that the entry point of the ramp is 7 feet far from the building.

so BC= 7 feet

So we have to find the distance between the ground and the end of the ramp i.e. we have to find the length of AB.

So from the figure given below, it is clear that ΔABC is a right-angled triangle.

As we know tan θ= opposite side/ adjacent side

⇒ tan 8°= AB/ BC

⇒ tan 8°= AB/7

⇒ AB= 7 tan 8°

⇒ AB= 0.98 feet

Therefore the distance between the ground and the end of the ramp is 0.98 feet.

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