Right Triangles and Trigonometry Practice

Sample questions

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1. Sample 1difficulty 2/5

   In a right triangle, the leg opposite $\theta$ is $7$ and the leg adjacent is $24$. What is $\tan\theta$?

   • A

     $\frac{24}{7}$

   • B

     $\frac{7}{24}$

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   • C

     $\frac{24}{25}$

   • D

     $\frac{7}{25}$

   Why

   $\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{7}{24}$.

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2. Sample 2difficulty 2/5

   In a right triangle, the leg adjacent to angle $\theta$ is $8$ and the hypotenuse is $17$. What is $\cos\theta$?

   • A

     $\frac{8}{17}$

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   • B

     $\frac{17}{8}$

   • C

     $\frac{15}{17}$

   • D

     $\frac{8}{15}$

   Why

   $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{8}{17}$.

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3. Sample 3difficulty 2/5

   What is the value of $\tan(45°)$?

   • A

     $1$

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   • B

     $\sqrt{2}$

   • C

     $\frac{1}{2}$

   • D

     $0$

   Why

   $\tan(45°)=\frac{\sin 45°}{\cos 45°}=1$.

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4. Sample 4difficulty 2/5

   In a right triangle, opposite side is $5$, adjacent is $12$. What is the hypotenuse?

   • A

     $13$

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   • B

     $\sqrt{169}/2$

   • C

     $17$

   • D

     $15$

   Why

   Hypotenuse $=\sqrt{25+144}=\sqrt{169}=13$.

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5. Sample 5difficulty 2/5

   In a 45-45-90 triangle, each leg has length 5. What is the length of the hypotenuse?

   • A

     $5\sqrt{3}$

   • B

     10

   • C

     $5\sqrt{2}$

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   • D

     $\sqrt{10}$

   Why

   In a 45-45-90 triangle, the ratio of leg : leg : hypotenuse is $1:1:\\sqrt{2}$. So hypotenuse $= 5\\sqrt{2}$.

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