1. When you look down from the top of a building at an angle of 63degrees, you will see a man reading a newspaper. If the building is 50m high, how far is the man from the building?
2. A plane takes off at an angle of 15deg20'. How high will it have risen after it has flown a slant distance of
20 000 m?
a, Tan 27=50/d solve for d
b. sinAngle=h/20,000
solve for h.
50/x = tan 63
x/20000 = sin 15.33
To solve these problems, we will be using trigonometric ratios, specifically the tangent function. The tangent function relates the opposite side length of a right triangle to the adjacent side length.
1. To find the distance between the man and the building, we need to find the length of the adjacent side.
We know that the angle of depression from the top of the building is 63 degrees. Let's call the distance between the man and the building 'x'. The height of the building is 50m.
Using the tangent function, we can write:
tan(63 degrees) = height of the building / distance between the man and the building
tan(63 degrees) = 50m / x
To solve for 'x', we rearrange the equation:
x = 50m / tan(63 degrees)
Using a calculator, evaluate the tangent of 63 degrees, and then divide 50m by that value. The result will be the distance between the man and the building.
2. Similarly, to find the height the plane will have risen after flying a slant distance of 20,000m, we need to find the length of the opposite side.
We know that the angle of elevation is 15 degrees 20 minutes. Let's call the height the plane has risen 'h'. The slant distance traveled is 20,000m.
Using the tangent function, we can write:
tan(15 degrees 20 minutes) = height of the plane / slant distance traveled
tan(15 degrees 20 minutes) = h / 20,000m
To solve for 'h', we rearrange the equation:
h = 20,000m * tan(15 degrees 20 minutes)
Using a calculator, evaluate the tangent of 15 degrees 20 minutes, and then multiply 20,000m by that value. The result will be the height the plane has risen.