Chapter 13: Q34. (page 707)

Solve triangle ABC using the given measurements if $A = 45 {}^{\circ}, C = 90 {}^{\circ}{and} c = 7 \sqrt{2}$ . Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short Answer

Expert verified

The solution for triangle ABC is $a = 7, b = 7 and B = 45 °$ .

Step by step solution

Step 1. Write down the given parameters of triangle.

The given triangle ABC is shown below whose parameters are represented as $A = 45 {}^{\circ}, C = 90 {}^{\circ}{and} c = 7 \sqrt{2}$ .

Step 2. Calculation.

In triangle ABC, $A = 45 {}^{\circ}, C = 90 {}^{\circ}{and} c = 7 \sqrt{2}$ . Therefore, $∠ B = 45 °$ by angle sum property.

Now, trigonometric ratios,

$\begin{matrix} \sin B = \frac{b}{c} \\ \sin 45 ° = \frac{b}{7 \sqrt{2}} \\ b = 7 \sqrt{2} \sin (45 °) \\ b = 7 \end{matrix}$

Now, in right triangle ABC by Pythagoras Theorem.

$\begin{matrix} c^{2} = a^{2} + b^{2} gives, \\ {(7 \sqrt{2})}^{2} = a^{2} + {(7)}^{2} \\ a^{2} = {(7 \sqrt{2})}^{2} - {(7)}^{2} \\ a = \sqrt{{(7 \sqrt{2})}^{2} - {(7)}^{2}} \\ a = 7 \end{matrix}$

Step 3. Conclusion.

Thesolution for triangle ABC, is $a = 7, b = 7 and B = 45 °$ .

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Solve triangle ABC using the given measurements if $A = 45 {}^{\circ}, C = 90 {}^{\circ}{and} c = 7 \sqrt{2}$ . Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short Answer

Step by step solution

Step 1. Write down the given parameters of triangle.

Step 2. Calculation.

Step 3. Conclusion.

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Solve triangle ABC using the given measurements if A=45,∘C=90and∘c=72. Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short Answer

Step by step solution

Step 1. Write down the given parameters of triangle.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Solve triangle ABC using the given measurements if $A = 45 {}^{\circ}, C = 90 {}^{\circ}{and} c = 7 \sqrt{2}$ . Round measure of sides to the nearest tenth and measures of angles to nearest degree.