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3 years ago

1. To calculate the height of a tree,

Mathematics

2 answers:

weqwewe [10]3 years ago

8 0

Answer:

h ≈ 30.10 ft

Step-by-step explanation:

Marie measures the angle of elevation from a point A to a tree as 34° . She works 10 ft directly towards the tree and discovered the new angle of elevation is 41°. The height of the tree can be computed below.

let

a = distance from point B to the tree

h = height of the tree

The right angle triangle formed from point B, we can use tan to find the height of the tree.

tan 41° = opposite /adjacent

tan 41° = h/a

cross multiply

h = a tan 41°

The right angle formed from point A

tan 34° = opposite/adjacent

tan 34° = h/(a + 10)

(a + 10)tan 34° = h

Therefore,

a tan 41° = (a + 10)tan 34°

0.8692867378

a = 0.6745085168(a + 10)

0.8692867378a = 0.6745085168a + 6.7450851684

collect like terms

0.8692867378a - 0.6745085168a = 6.7450851684

0.194778221a = 6.7450851684

a = 6.7450851684/0.194778221

a = 34. 629565532 ft

height of the tree can be find with

h = a tan 41°

h = 34. 629565532 × 0.8692867378

h = 30.103022053 ft

h = 30.10 ft

PilotLPTM [1.2K]3 years ago

4 0

72 I think if not try 41+34=x

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How to solve such questions?

Such Questions can be easily solved just by some Algebraic manipulations and simplifications. We just try to make our expression in the form which question asks us. This is the best method to solve such questions as it will definitely lead us to correct answers. One such method is completing the square method.

Completing the square is a method that is used for converting a quadratic expression of the form $ax^{2} + bx + c$ to the vertex form

$a(x - h)^{2} + k$ . The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: $a(x + m)^{2} + n$ , such that the left side is a perfect square trinomial