Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

A hiker whose eyes are 5.5 feet above the ground stands 25 feet from the base of a redwood tree. She looks up at an angle of 71 degrees to see the top of the tree. To the nearest tenth of a foot, what is the height of the tree?

Sagot :

anijlin
If you draw out a diagram of the situation, the height of the person is 5.5 feet, standing 25 feet away from the tree. then the person looks up at a 71 degree angle with the top of the tree, it should look like a right triangle on top of a rectangle. 

We know the angle she's looking at (71 degrees) and the side adjacent to the angle (the distance she is away from the tree, 25 feet). Using tangent we can solve for the opposite side. 

tan(71 degrees) = x ÷ 25
25 tan (71 degrees) = x
x is about 72.6 feet 

that's the height from her eyes to the top of the tree. 
To get the height of the tree you add how high above the ground her eyes are (5.5 feet) to x (72.6 feet) 

72.6 + 5.5 = 78.1 feet

that should be the height of the tree
kakie
Tan of a 71 degree angle = 71 tan/1=72 feet + 5.5 feet (because of the height of the hiker's eyes) = 78.1 feet
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.