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Trigonometry
Question

What is the distance from Kareem to the house?Kare...

What is the distance from Kareem to the house?

Kareem and Amy are standing on a riverbank, \( 150 \) meters apart, at points \( A \) and \( B \) respectively. (See the figure below.) They want to know the distance from Kareem to a house located across the river at point \( C \) . Kareem measures angle \( A \) (angle \( B A C \) ) to be \( 55 ^ { \circ } \) , and Amy measures angle \( B \) (angle \( A B C \) ) to be \( 74 ^ { \circ } \) . What is the distance from Kareem to the house? Round your answer to the nearest tenth of a meter. 

Answer

\(\angle C= 180- 55- 74= 51\\ \frac { \sin 51} { 150} = \frac { \sin 74} { d} \\ d= 185.5\)

Solution
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