A hiker standing at point G wants to estimate the distance across the lake to point H, which is directly north of her location.

Question

2 years ago

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A hiker standing at point G wants to estimate the distance across the lake to point H, which is directly north of her location.

She walks 650 feet west to point F. She measures the angle from point F to point H to be 84º north of east. Find the distance across the lake to the nearest tenth of a foot. a. 68.3 feet b. 646.4 feet c. 655.4 feet d. 6,184.4 feet

Mathematics

1 answer:

riadik2000 [5.3K] · Answer 1 · 2022-03-25T13:55:39+03:00

Answer:

D

Step-by-step explanation:

The diagram is attached.

Looking at the diagram, we want the side "opposite" of the angle given and the side "adjacent" is given.

Which ratio relates opposite and adjacent? It is Tan.

We can use trigonometry and tan ratio to solve for the distance "x":

$Tan(84)=\frac{x}{650}\\x=Tan(84)*650\\x=6184.4$

D is the correct answer.