To find the length of the diagonal, we need to calculate the length of the base first and then use the value to calculate the diagonal since we are given the value of height of the triangle.

<h3>Pythagorean Theorem</h3>

This theorem is used to find the missing side of a right angle triangle given that we have the length of two sides.

To calculate the base of the triangle, let's use Pythagorean theorem here

$x^2 = y^2 + z^2\\x^2 = 2^2 + 3^2\\x^2 = 4 + 9 \\x^2 = 13\\x = \sqrt{13} \\x = 3.61$

Having the length of the base, let's consider the height of the triangle which is 6 and substitute the values.

$d^2 = 6^2 + 3.61^2\\d^2 = 36 + 13.0321\\d^2 = 49.0321\\d = \sqrt{49.0321} \\d = 7.00$

From the calculations above, the values of the triangle are

diagonal = 7
base = 3.61
height = 6

Learn more on pythagorean theorem here;

brainly.com/question/231802

#SPJ1

7 0

1 year ago

Two people are 100 feet apart on opposite sides of a tree. The angles of elevation from the people to the top of the tree are 30

cricket20 [7]

We need to solve for the height of the tree given two angles and distance between the two observers. See attached drawing for a better understanding of the problem.
We derive to equations using SOH CAH TOA such as below:
sin30 = h / x
sin 45 = h / (100-x)

sin 45 (100-x) = xsin30
70.71 - 0.71x = 0.5x
70.71 = 1.21 x
x = 58.44

Solving for h, we have:
h = xsin30
h = 58.44 sin30
h = 29.22

The height of the tree is 29.22 feet.

4 0

3 years ago

Read 2 more answers