The angle of elevation to a nearby tree from a point on the ground is measured to be 69∘ . How tall is the tree if the point on the ground is 35 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.

The tree is approximately 91.2 ft tall.

Step-by-step explanation:

Hi there!

We're told:

- angle of elevation = 69 degrees

- there is a point 35 feet from the tree

If we were to draw this out, it would appear to be a right angle triangle. See the picture below.

Now, to solve for the height of the tree, we can use the sine law:

where a and b are two sides of a right triangle and A and B are the respective opposite angles

Let the height of the tree = h.

Side h is opposite of the angle measuring 69 degrees:

Let the angle opposite of the side measuring 35 feet = A.

Because the sum of a triangle's interior angles is 180 degrees, we know that A=180-90-69=21 degrees.

Use the sine law:

Therefore, the tree is approximately 91.2 ft tall.

I hope this helps!

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.