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High School Math : Triangles

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Example Questions

Example Question #4 : Right Triangles

Which set of sides could make a right triangle?

Possible Answers:

6, 7, 8

4, 6, 9

10, 12, 16

9, 12, 15

Correct answer:

9, 12, 15

Explanation:

By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.

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Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

A right triangle with a base of 12 and hypotenuse of 15 is shown below. Find x.

Screen_shot_2013-03-18_at_10.29.39_pm

Possible Answers:

3.5

5.5

4.5

Correct answer:

Explanation:

Using the Pythagorean Theorem, the height of the right triangle is found to be = √(〖15〗²–〖12〗²) = 9, so x=9 – 5=4

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Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has sides of 36 and 39(hypotenuse). Find the length of the third side

Possible Answers:

33√2

12 √6

Correct answer:

Explanation:

use the pythagorean theorem:

a² + b² = c² ; a and b are sides, c is the hypotenuse

a² + 1296 = 1521

a² = 225

a = 15

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Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

Bob the Helicopter is at 30,000 ft. above sea level, and as viewed on a map his airport is 40,000 ft. away. If Bob travels in a straight line to his airport at 250 feet per second, how many minutes will it take him to arrive?

Possible Answers:

2 hours and 30 minutes

4 hours and 0 minutes

3 minutes and 50 seconds

1 hour and 45 minutes

3 minutes and 20 seconds

Correct answer:

3 minutes and 20 seconds

Explanation:

Draw a right triangle with a height of 30,000 ft. and a base of 40,000 ft. The hypotenuse, or distance travelled, is then 50,000ft using the Pythagorean Theorem. Then dividing distance by speed will give us time, which is 200 seconds, or 3 minutes and 20 seconds.

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Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has two sides, 9 and x, and a hypotenuse of 15. What is x?

Possible Answers:

Correct answer:

Explanation:

We can use the Pythagorean Theorem to solve for x.

9² + x² = 15²

81 + x² = 225

x² = 144

x = 12

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Example Question #5 : How To Find The Length Of The Side Of A Right Triangle

The area of a right traingle is 42. One of the legs has a length of 12. What is the length of the other leg?

Possible Answers:

$7$ $\displaystyle 7$

$11$ $\displaystyle 11$

$9$ $\displaystyle 9$

$6$ $\displaystyle 6$

$5$ $\displaystyle 5$

Correct answer:

$7$ $\displaystyle 7$

Explanation:

$Area= \frac{1}{2}\times base\times height$ $\displaystyle Area= \frac{1}{2}\times base\times height$

$42=\frac{1}{2}\times base\times 12$ $\displaystyle 42=\frac{1}{2}\times base\times 12$

$42=6\times base$ $\displaystyle 42=6\times base$

$base=7$ $\displaystyle base=7$

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Example Question #141 : Plane Geometry

Triangle

$\left ( \bigtriangleup ABC \textup{ is a right triangle where } \angle B \textup{ is a right angle}\right)$

If $\angle A=30^{\circ}$ $\displaystyle \angle A=30^{\circ}$ and $\overline{AB}=4$ $\displaystyle \overline{AB}=4$ , what is the length of $\overline{BC}$ $\displaystyle \overline{BC}$ ?

Possible Answers:

$\displaystyle 4$

$\frac{4\sqrt{3}}{3}$ $\displaystyle \frac{4\sqrt{3}}{3}$

$\displaystyle 3$

$\frac{4}{3}$ $\displaystyle \frac{4}{3}$

Correct answer:

$\frac{4\sqrt{3}}{3}$ $\displaystyle \frac{4\sqrt{3}}{3}$

Explanation:

AB is the leg adjacent to Angle A and BC is the leg opposite Angle A.

Since we have a $30^{\circ}-60^{\circ}-90^{\circ}$ $\displaystyle 30^{\circ}-60^{\circ}-90^{\circ}$ triangle, the opposites sides of those angles will be in the ratio $x-x\sqrt{3}-2x$ $\displaystyle x-x\sqrt{3}-2x$ .

Here, we know the side opposite the sixty degree angle. Thus, we can set that value equal to $x\sqrt{3}$ $\displaystyle x\sqrt{3}$ .

$4=x\sqrt{3}$ $\displaystyle 4=x\sqrt{3}$

$\frac{4}{\sqrt{3}}=\frac{x\sqrt{3}}{\sqrt{3}}$ $\displaystyle \frac{4}{\sqrt{3}}=\frac{x\sqrt{3}}{\sqrt{3}}$

$\frac{4}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}=x$ $\displaystyle \frac{4}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}=x$

$x=\frac{4\sqrt{3}}{3}$ $\displaystyle x=\frac{4\sqrt{3}}{3}$

which also means

$\overline{BC}=\frac{4\sqrt{3}}{3}$ $\displaystyle \overline{BC}=\frac{4\sqrt{3}}{3}$

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Example Question #7 : How To Find The Length Of The Side Of A Right Triangle

Solve for x.

Possible Answers:

Correct answer:

Explanation:

Use the Pythagorean Theorem. Let a = 8 and c = 10 (because it is the hypotenuse)

$\small a^2+x^2=c^2$ $\displaystyle \small a^2+x^2=c^2$

$\small 8^2+x^2=10^2$ $\displaystyle \small 8^2+x^2=10^2$

$\small 64+x^2=100$ $\displaystyle \small 64+x^2=100$

$\small x^2=100-64=36$ $\displaystyle \small x^2=100-64=36$

$\small x=6$ $\displaystyle \small x=6$

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Example Question #21 : Right Triangles

Solve for $\small x$ $\displaystyle \small x$ .

Possible Answers:

$\displaystyle 3$

$\displaystyle 19$

$\displaystyle 9$

$\displaystyle 20$

Correct answer:

$\displaystyle 9$

Explanation:

Use the Pythagorean Theorem to solve for the missing side of the right triangle.

$\displaystyle a^2+b^2=c^2$

In this triangle, $\small a=x,\ b=12,\ c=15$ $\displaystyle \small a=x,\ b=12,\ c=15$ .

$\displaystyle x^2+12^2=15^2$

Now we can solve for $\small x$ $\displaystyle \small x$ .

$\displaystyle x^2+144=225$

x^2=81 $\displaystyle x^2=81$

x=9 $\displaystyle x=9$

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Example Question #21 : Right Triangles

Solve for $\small x$ $\displaystyle \small x$ .

Possible Answers:

110 $\displaystyle 110$

$110\sqrt2$ $\displaystyle 110\sqrt2$

$55\sqrt2$ $\displaystyle 55\sqrt2$

$110\sqrt3$ $\displaystyle 110\sqrt3$

Correct answer:

110 $\displaystyle 110$

Explanation:

This image depicts a 30-60-90 right triangle. The length of the side opposite the smallest angle is half the length of the hypotenuse.

$a^2+b^2=c^2\rightarrow (a)^2+(a\sqrt{3})^2=(2a)^2$ $\displaystyle a^2+b^2=c^2\rightarrow (a)^2+(a\sqrt{3})^2=(2a)^2$

2a=220 $\displaystyle 2a=220$

$a=\frac{220}{2}=110$ $\displaystyle a=\frac{220}{2}=110$

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High School Math : Triangles

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #4 : Right Triangles

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

Example Question #5 : How To Find The Length Of The Side Of A Right Triangle

Example Question #141 : Plane Geometry

Example Question #7 : How To Find The Length Of The Side Of A Right Triangle

Example Question #21 : Right Triangles

Example Question #21 : Right Triangles

All High School Math Resources

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