All categories

3 years ago

When the angle of elevation of the sun is 78 degrees, a tree casts a 13 foot shadow. How tall is the tree?

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

4 0

Answer: 61.16 ft

Step-by-step explanation:

We can think in this situation as a triangle rectangle.

where:

The height of the tree is one cathetus

The shadow of the tree is the other cathetus.

We know that the angle of elevation of the sun is 78°, an angle of elevation is measured from the ground, then the adjacent cathetus to this angle is the shadow of the tree. And the opposite cathetus will be the height of the tree.

Now we can remember the relationship:

Tg(A) = (opposite cathetus)/(adjacent cathetus)

Where:

A = 78°

Adjacent cathetus = 13ft

opposite cathetus = height of the tree = H

Then we have the equation:

Tg(78°) = H/13ft

Tg(78°)*13ft = H = 61.16 ft

You might be interested in

Find the value of 3 square root of 1000

irga5000 [103]

The answer to this is 10

5 0

3 years ago

Read 2 more answers

What is the percent of 120 minus 94

lyudmila [28]

The correct answer is 26%

6 0

3 years ago

Find the value of in the triangle shown below<br><br> 9, 7, and x around the triangle

enot [183]

Answer:

5.66 units

Step-by-step explanation:

A's per our discussion, x is a leg of right triangle.

Therefore, by Pythagoras theorem:

$x = \sqrt{ {9}^{2} - {7}^{2} } \\ = \sqrt{81 - 49} \\ = \sqrt{32}$

$x = \sqrt{ {16}^{2} - {12}^{2} } \\ = \sqrt{256 - 144} \\ = \sqrt{112}$

4 0

3 years ago

Solve the system by using a matrix equation (Picture provided)

Katyanochek1 [597]

Answer:

Option b is correct (8,13).

Step-by-step explanation:

7x - 4y = 4

10x - 6y =2

it can be represented in matrix form as $\left[\begin{array}{cc}7&-4\\10&-6\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}4\\2\end{array}\right]$

A= $\left[\begin{array}{cc}7&-4\\10&-6\end{array}\right]$

X= $\left[\begin{array}{c}x\\y\end{array}\right]$

B= $\left[\begin{array}{c}4\\2\end{array}\right]$

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (7*-6) - (-4*10)

= (-42)-(-40)

= (-42) + 40 = -2

so, |A| = -2

Adj A= $\left[\begin{array}{cc}-6&4\\-10&7\end{array}\right]$

A⁻¹ = $\left[\begin{array}{cc}-6&4\\-10&7\end{array}\right]$ / -2

A⁻¹ = $\left[\begin{array}{cc}3&-2\\5&-7/2\end{array}\right]$

X= A⁻¹ B

X= $\left[\begin{array}{cc}3&-2\\5&-7/2\end{array}\right] *\left[\begin{array}{c}4\\2\end{array}\right]$

X= $\left[\begin{array}{c}(3*4) + (-2*2)\\(5*4) + (-7/2*2)\end{array}\right]$

X= $\left[\begin{array}{c}12-4\\20-7\end{array}\right]$

X= $\left[\begin{array}{c}8\\13\end{array}\right]$

x= 8, y= 13

solution set= (8,13).

Option b is correct.

3 0

3 years ago

When trying to find the best deal for items, you should ____

kodGreya [7K]

Question 1:

All provided options would give the best deal on an item

Answer: Option d [all of the above]

Question 2:

When an item's price is knocked off by 15%, it means the item has only 85% of its original value left to pay. Hence, a discount of 15% means multiplying the original price by 85%

Answer: option C

6 0

3 years ago

Read 2 more answers