Question

The given diagram shows the parts of a right triangle with an altitude to the hypotenuse. Using the two given​ measures, find the other four.

Answer 1

I only could find part of the triangle sorry, but u1 is 2 radical 2

Answer 2

The value of h, is 4, $\rm s_2$ is 2, and the value of $\rm u_1$ and $\rm u_2$ is $2\sqrt{2}$.

Given

The given diagram shows the parts of a right triangle with an altitude to the hypotenuse.

Right - Angle Triangle;

To solve this problem, we have to use some basic formulas in a right-angle triangle such as trigonometric ratios and Pythagoreans theorem.

$\rm h=s_1+s_2\\\\ s_1=2\\\\ a=2$

On the top of the triangle, we have another right-angle divided into two. This makes each side equal 90/2 = 45 degrees.

Using the length of a, we can solve for u1 or u2 using the Pythagorean theorem.

$\rm u_1^2=s_1^2+a^2\\\\ u_1^2=2^2+2^2\\\\ u_1^2=4+4\\\\ u_1^2=8\\\\ u_1=2\sqrt{2}$

Then,

The value of h, is;

$\rm u_1=\sqrt{s_1 \times h}\\\\2\sqrt{2}=\sqrt{2h} \\\\\text{squaring on both sides}\\\\4\times 2=2h\\\\h=\dfrac{8}{2}\\\\h=4$

Then,

The value of $\rm s_1$ is;

$\rm h=s_1+s_2\\\\ 4=2+s_2\\\\s_2=4-2\\\\s_2=2$

The value of $\rm u_2$ is;

$\rm u_2^2=s_2^2+a^2\\\\ u_2^2=2^2+2^2\\\\ u_2^2=4+4\\\\ u_2^2=8\\\\ u_2=2\sqrt{2}$

Hence, the required value of h is 4, $\rm s_2$ is 2, and the value of $\rm u_1$ and $\rm u_2$ is $2\sqrt{2}$.

To know more about the right triangle click the link given below.

https://brainly.com/question/4364353