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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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:

$7$

$11$

$9$

$6$

$5$

Correct answer:

$7$

Explanation:

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

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

$42=6\times base$

$base=7$

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Example Question #111 : Sat Mathematics

Triangle

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

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

Possible Answers:

$\frac{4}{3}$

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

Correct answer:

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

Explanation:

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

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

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

$4=x\sqrt{3}$

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

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

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

which also means

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

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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)

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

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

$\small 64+x^2=100$

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

$\small x=6$

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Example Question #21 : Right Triangles

Solve for $\small x$ .

Possible Answers:

Correct answer:

Explanation:

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

a^2+b^2=c^2

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

x^2+12^2=15^2

Now we can solve for $\small x$ .

x^2+144=225

x^2=81

x=9

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Example Question #21 : Right Triangles

Solve for $\small x$ .

Possible Answers:

110

$110\sqrt2$

$55\sqrt2$

$110\sqrt3$

Correct answer:

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.

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

2a=220

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

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Example Question #23 : Right Triangles

Given a right triangle, solve for the missing leg if one leg is 12 and the hypotenuse is 13.

Possible Answers:

17.69

Correct answer:

Explanation:

Since the traingle is a right traingle, we can use the Pythagorean Theorem to solve for the missing leg:

a^2 + b^2 = c^2

a=12 and the hypotenuse c=13

(12)^2 + b^2 = (13)^2

b^2 = (13)^2- (12)^2

b^2 = 169- 144

b^2 = 25

b = 5

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Example Question #141 : Plane Geometry

Points $\dpi{100} \small A$ , $\dpi{100} \small B$ , and $\dpi{100} \small C$ are collinear (they lie along the same line). $\angle ACD = 90^{\circ}$ , $\angle CAD=30^{\circ}$ , $\angle CBD=60^{\circ}$ , $\overline{AD}=4$

Find the length of segment $\overline{BD}$ .

Possible Answers:

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

$\frac{\sqrt{3}}{2}$

$\frac{2\sqrt{3}}{3}$

$2$

$2\sqrt{3}$

Correct answer:

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

Explanation:

The length of segment $\overline{BD}$ is $\frac{4\sqrt{3}}{3}$

Note that triangles $\dpi{100} \small ACD$ and $\dpi{100} \small BCD$ are both special, 30-60-90 right triangles. Looking specifically at triangle $\dpi{100} \small ACD$ , because we know that segment $\overline{AD}$ has a length of 4, we can determine that the length of segment $\overline{CD}$ is 2 using what we know about special right triangles. Then, looking at triangle $\dpi{100} \small BCD$ now, we can use the same rules to determine that segment $\overline{BD}$ has a length of $\frac{4}{\sqrt{3}}$

which simplifies to $\frac{4\sqrt{3}}{3}$ .

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Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

$\textup{What is the length of the hypotenuse of a right triangle with legs of lengths 10 and 15?}$

Possible Answers:

$13\sqrt{5}$

$5\sqrt{13}$

$6\sqrt{13}$

Correct answer:

$5\sqrt{13}$

Explanation:

$\textup{Pythagorean Theorum: }a^{2}+b^{2}= c^{2}\;\;\;\;\;\;10^{2}+15^{2}=c^{2}$

$100+225=c^{2}\;\;\;\;325=c^{2}\;\;\;\;\;\sqrt{325}=c\;\;\;\;\sqrt{25}\times\sqrt{13}=c$

$5\sqrt{13}=c$

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Example Question #23 : Right Triangles

Rt_triangle_letters

If angle $c=90^\circ$ , Y=3 and Z=4 , what is the value of ?

Possible Answers:

12.5

Correct answer:

Explanation:

Once we see that $c=90^\circ$ , we know that we're working with a right triangle and that will be the hypotenuse.

At this point we can use the Pythaogrean theorem ( a^2+b^2=c^2 ) or, in this case: Y^2+Z^2=X^2 .

Plug in our given values to solve:

Y^2+Z^2=X^2

3^2+4^2=X^2

9+16=X^2

25=X^2

$\sqrt{25}=\sqrt{X^2}$

5=X

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Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Rt_triangle_letters

If angle $c=90^\circ$ , X = 13 and Y = 12 , what is the value of ?

Possible Answers:

169

144

17.69

Correct answer:

Explanation:

Once we see that $c=90^\circ$ , we know we're working with a right triangle and that will be the hypotenuse.

At this point we can use the Pythaogrean theorem ( a^2+b^2=c^2 ) or, in this case: Y^2+Z^2=X^2 .

Plug in our given values to solve:

Y^2+Z^2=X^2

12^2+Z^2=13^2

144+Z^2=169

Subtract 144 from both sides:

Z^2=25

$\sqrt{Z^2}=\sqrt{25}$

Z=5

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

Example Question #111 : Sat Mathematics

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

Example Question #23 : Right Triangles

Example Question #141 : Plane Geometry

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #23 : Right Triangles

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

All High School Math Resources

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