a) The angle shown as 45.5 deg in the figure should read 45.8 deg.
tan 45.5 deg = y/175
y = 175 ft * tan 45.8 deg = 180 ft
tan 34.4 deg = z/175
z = 175 ft * tan 34.4 deg = 120 ft
y - z = 180 ft - 120 ft = 60 ft
The height of Pres. Washington's face is 60 ft.
b)
Area of 1/8 of a 12" pizza: 1/8 * pi * (12/2 ")^2 = 14.1 in.^2
Area of 1/6 of a 10" pizza: 1/6 * pi * (10/2 ")^2 = 13.1 in.^2
The slice of the 12" pizza is larger.
c)
A bearing of 27 deg is 90 - 27 = 63 deg counterclockwise from due East.
A bearing of 117 deg is 117 - 90 = 27 deg clockwise from due East.
The two bearing directions make a 90 deg angle between them.
55 km/h for 2 hours = 110 km
60 km/h for 1.5 hours = 90 km
The two amounts traveled are 110 km and 90 km at 90 deg from each other. They form the legs of a right triangle. The distance traveled from the starting point is the hypotenuse of the right triangle formed by the the two distances traveled.
(90 km)^2 + (110 km)^2 = d^2
d = 142 km
The distance traveled is 142 km.