Answer:
(a) height: 44.5 m
(b) shadow: 71.2 m
Step-by-step explanation:
You want building height and shadow length for angles of elevation 56° and 32°, given the shadow is 30 m when elevation is 56°.
Trig relation
The building height and shadow length are the sides opposite and adjacent (respectively) to the elevation angle in the right triangle that models the geometry. The trig function that relates these sides to the angle is the tangent function:
Tangent = Opposite/Adjacent
Application
(a) building height
Using the tangent relation, we have ...
tan(56°) = (height)/(30 m)
height = (30 m)(tan(56°)) ≈ 44.4768 m
The height of the building is about 44.5 meters.
(b) shadow length
Using the same relation with the building height known, we have ...
tan(32°) = (44.4768 m)/(shadow)
shadow = (44.4768 m)/tan(32°) ≈ 71.1778 m
The length of the shadow at an angle of 32° is about 71.2 m.
