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Alex777 [14]
3 years ago
8

Consider the right triangle ABC given below:

Mathematics
2 answers:
Gre4nikov [31]3 years ago
4 0

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  

VLD [36.1K]3 years ago
3 0
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.
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