from a point 50 m from the base of a cliff, a surveyor measures the angle of elevation to the top of the cliff as 73.2 degrees. how tall is the cliff to the nearest metre.

tan 73.2 = h/50

so
h = 50 tan 73.2

Tan 73.2 = h/50

Bring 50 onto the left side
50 Tan 73.2 = h
165.6 = h
Round it to closest decimal place
166 = h

To determine the height of the cliff, we can use the tangent function, which relates the angle of elevation to the height and distance. The tangent of an angle is equal to the height divided by the distance.

Let's call the height of the cliff "h" and the distance from the point to the base of the cliff "d."

In this case, we are given the value of the angle of elevation (73.2 degrees) and the distance (50 m). We need to solve for the height ("h").

Using trigonometry, we can set up the equation:

tan(angle) = height / distance

Substituting in the known values:

tan(73.2 degrees) = h / 50 m

Now, we need to isolate "h" by multiplying both sides of the equation by 50 m:

50 m * tan(73.2 degrees) = h

Using a scientific calculator, calculate the tangent of 73.2 degrees:

tan(73.2 degrees) ≈ 3.0141

Substituting this value into the equation:

50 m * 3.0141 ≈ h

h ≈ 150.7 m

Therefore, the height of the cliff is approximately 150.7 meters to the nearest meter.