Question

Consider the right triangle ABC given below:

Answer 1

Answer:

Part A)  The length of the hypotenuse of triangle ABC is

 $AB=\frac{40\sqrt{3}}{3}\ units$  

Part B) The length of the shorter leg of triangle ABC is

$AC=\frac{20\sqrt{3}}{3}\ units$

Part C) The length of the longer leg of triangle ABC is

$BC=20\ units$

Step-by-step explanation:

see the attached figure  to better understand the problem

Step 1

Find the length of the longer leg of triangle ABC  (side BC)

we know that  

In the right triangle DBC  

$sin(30\°)=\frac{DC}{BC}$

substitute the values and solve for BC

$sin(30\°)=\frac{10}{BC}$

$BC=10/sin(30\°)=20\ units$

Step 2

Find the length of the shorter leg of triangle ABC  (side AC)

we know that  

In the right triangle ACD

$sin(60\°)=\frac{DC}{AC}$

substitute the values and solve for AC

$sin(60\°)=\frac{10}{AC}$

$AC=10/sin(60\°)=\frac{20\sqrt{3}}{3}\ units$

Step 3

Find the length of the hypotenuse of triangle ABC (side AB)

Applying the Pythagoras theorem

$AB^{2}=BC^{2}+AC^{2}$

we have

$AC=\frac{20\sqrt{3}}{3}\ units$

$BC=20\ units$

substitutes

$AB^{2}=20^{2}+(\frac{20\sqrt{3}}{3})^{2}$

$AB^{2}=400+(\frac{400}{3})$

$AB^{2}=(\frac{1600}{3})$

$AB=\frac{40\sqrt{3}}{3}\ units$  

Answer 2

I do not know what you mean by the wording of some of these questions, so I will just give you the formula and tell you how to apply it. The formula of the Pythagorean Theorem is a^2 + b^2 = c^2. a and b are the two sides adjecent to the right angle (in the corner). c is the side opposite the right angle. So, to get c you would have to add sides a and b but with each of them to the second power. Then, you would find the square root of the sum (you can do this with a calculator). To find sides a or b, subtract a or b (whichever one available) to the second power from c to the second power. Then find the square root of the sum. That is all I know how to do, so combine this knowledge with yours to see if you can solve it. If you have any questions about what I already know, feel free to ask. You can also ask for an example. If you have a question about something that I have not explained, look it up on the internet, or hopefully you can find someone who can help you. I hope this helps.