Draw a diagram.
TriangleABC:Triangle ABC:TriangleABC:
∠BAC=13°\angle BAC= 13 \degree∠BAC=13°
tan(∠BAC)=tan13°=BCAB=50−hz\tan (\angle BAC) = \tan 13\degree = \dfrac{BC}{AB} = \dfrac{50-h}{z}tan(∠BAC)=tan13°=ABBC=z50−h
z=50−htan13°z = \dfrac{50-h}{\tan 13\degree}z=tan13°50−h
h=50−tan13°∗zh = 50 - \tan 13\degree*zh=50−tan13°∗z (1)(1)(1)
TriangleABD:Triangle ABD:TriangleABD:
∠BAD=35°\angle BAD= 35 \degree∠BAD=35°
tan(∠BAD)=tan35°=BDAB=50z\tan (\angle BAD) = \tan 35\degree = \dfrac{BD}{AB} = \dfrac{50}{z}tan(∠BAD)=tan35°=ABBD=z50
z=50tan35°z = \dfrac{50}{\tan 35\degree}z=tan35°50 (2)(2)(2)
Substitute(2)to(1):Substitute (2) to (1):Substitute(2)to(1):
h=50−tan13°∗50tan35°h = 50 - \tan 13\degree*\dfrac{50}{\tan 35\degree}h=50−tan13°∗tan35°50
h=33.5mh = 33.5 mh=33.5m
Height of the house is 33.5 m
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