Question

mark has a three legged dog named buddy. buddy has difficulty climbing stairs. mark wants to build a ramp so buddy can get on the deck. mark has an 8 ft plank he can use for the ramp. the deck is 4 ft off the ground. what is the measurement of the angle formed by the plank and the height of the deck?

Answer 1

To calculate the angle formed by the plank and the deck's height, use the sine function with the height as the opposite side (4 ft) and the plank as the hypotenuse (8 ft), resulting in an angle of approximately 30 degrees.

Step-by-step explanation:

The question asks for the measurement of the angle formed by the 8 ft ramp (the hypotenuse of a right-angled triangle) and the 4 ft height of the deck (one of the legs of the triangle). We can find this angle using trigonometry, specifically the sine function.

To find the angle, we use the formula:

sin(angle) = opposite / hypotenuse

In this case, the opposite is the height of the deck (4 ft), and the hypotenuse is the length of the plank (8 ft).

Calculation:

sin(angle) = 4 ft / 8 ft = 0.5

To find the angle, we take the inverse sine (arcsin) of 0.5, which is approximately 30 degrees.

Therefore, the measurement of the angle formed by the plank and the height of the deck is 30 degrees.