The tree is approximately 35.979 feet tall, computed using the sine rule.
The sine rule in a triangle can be shown as this.
A triangle ABC, with the values of the side BC = a, CA = b, and AB = b, follows the rule by:
(Sin A)/a = (sin B)/b = (sin C)/c.
In the question, we are informed about Tasha who is willing to measure the height of a tree, which grows at an angle of 85° with respect to the ground. Also, we are informed that when Tasha is 80 feet away from the base of the tree, then the angle from the ground to the top of the tree is 25°.
We are asked to find the height of the tree.
We first draw a triangle using the given details, AB being the tree, and C being the point where Tasha is.
We know ∠A = 180° - (∠B + ∠C) {By angle sum property of triangles)
or, ∠A = 180° - (85° + 25°) = 180° - 110° = 70°.
Now, by sine rule, we can say that:
(Sin A)/a = (sin B)/b = (sin C)/c.
or, (Sin 70°)/80 = (sin 85°)/b = (sin 25°)/c,
or, 0.93969262078/80 = 0.42261826174/c {We ignored the middle term as we only need the height of the tree, that is, c}
or, c = 0.42261826174*80/0.93969262078/80
or, c = 35.9792768309.
Therefore, the tree is approximately 35.979 feet tall, computed using the sine rule.
Learn more about the sine rule at
https://brainly.com/question/4372174
#SPJ2
