A tree casts a shadow that is 125 feet in length. The angle of elevation with the sun is 32°. What is the height of the tree?

Mathematics

1 answer:

Molodets [167]3 years ago

4 0

Answer:

Height of the tree is 78.11 feet.

Step-by-step explanation:

By applying the tangent rule in the right triangle formed,

Since, tanθ = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

tan(32)° = $\frac{h}{125}$

h = 125(tan32°)

h = 125(0.62487)

h = 78.109

≈ 78.11 ft

Height of the tree will be 78.11 feet.

You might be interested in

A=12h(b1+b2) solve for b1 please.

Papessa [141]

A = 12h(B1 + B2)
A = 12h(B1) + 12h(B2)
A - 12h(B2) = 12h(B1)

B1 = $\frac{A - 12h(B1)}{12h}$

6 0

3 years ago

Abigail bought some mangoes at 3 for GH¢ 0.90 and sold all at 4 for GH¢ 1.60.If she made a profit of GH¢ 35.00,how many mangoes

umka21 [38]

Answer:

Step-by-step explanation:

Total costs = 4 + (3 * 2) + 5 + 15

Total costs = 4 + 6 + 5 + 15

Total costs = $ 30

Substituting values we have:

Total change = 32 - 30

Total change = 2 $

6 0

3 years ago

The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?

egoroff_w [7]

Answer:

(1, 3)

Step-by-step explanation:

You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:

$-2x^2+4x=-1$ . Now we factor out the -2:

$-2(x^2-2x)=-1$ . Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:

$-2(x^2-2x+1)=-1-2$ . Simplifying gives us this:

$-2(x^2-2x+1)=-3$

On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:

$-2(x-1)^2+3=y$