Please help me with trigonometry, my teacher is no help and I don't understand. I'm not looking only for answers, need to learn how to do it

Question

A survey team was to measure the distance across a river over which a bridge is to be built. They set up a survey post on their side of the river directly across from a large tree on the other side. Then they walked downstream a distance that they measured to be 400 meters. From the downstream position, they sighted the survey post and then rotated their calibrated transit to the tree to find the sighting angle to be 31°. 

 

A. Determine the distance directly across the river, that is, from the survey post to the tree on the opposite bank. 

 

B. Determine the distance from the surveyors sighting point to the tree on the opposite bank.

 

please help me! 

Answer 1

(A)

 

This may be a little hard to see without a picture, but let us give it a try.  Think of yourself as looking down from the sky toward the ground.  You see a right triangle.  Its base is the unknown distance d that you want to solve for.  Its left side is 400 m.  Its hypotenuse is √(400² + d²) m.  The angle between the left side and the hypotenuse is 31°.

 

Then

 

tan31° = d / (400 m)

 

d = (400 m) tan31° ≅ 240.3 m

 

(B)

 

This is just the hypotenuse from part (A).

 

h = √(400² + d²) m = √(400² + 240.3²) m ≅ 466.6 m