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For the triangle shown in the figure below what are each of the following? (Let y = 28.0 m and r = 35.0 m. Assume the triangle is a right triangle.) X e + (a) the length of the unknown side (x) (b) the tangent of 0 (c) the sin of

For the triangle shown in the figure below what are each of the following? (Let y = 28.0 m and r = 35.0 m. Assume the triangle is a right triangle.) X e + (a) the length of the unknown side (x) (b) the tangent of 0 (c) the sin of

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter3: Multi-step Equations And Inequalities
Section: Chapter Questions
Problem 11PTTS
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**Title: Right Triangle Calculations** For the right triangle shown in the figure below, what are each of the following? (Let \( y = 28.0 \, \text{m} \) and \( r = 35.0 \, \text{m} \). Assume the triangle is a right triangle.) ![Right Triangle](image_link_here) **(a) The length of the unknown side (\( x \))** **(b) The tangent of \( \theta \)** **(c) The sine of \( \varphi \)** --- **Explanation of the Figure:** The diagram shows a right triangle with the hypotenuse \( r = 35.0 \, \text{m} \), one leg \( y = 28.0 \, \text{m} \), and an unknown leg \( x \). The angle opposite the leg \( y \) is labeled \( \theta \), and the angle opposite the unknown leg \( x \) is labeled \( \varphi \). **(a) Finding the length of the unknown side (\( x \)):** We use the Pythagorean Theorem which states: \[ r^2 = x^2 + y^2 \] Plugging in the given values: \[ 35.0^2 = x^2 + 28.0^2 \] \[ 1225 = x^2 + 784 \] Subtracting 784 from both sides: \[ 441 = x^2 \] Taking the square root of both sides: \[ x = \sqrt{441} \] \[ x = 21.0 \, \text{m} \] **(b) Finding the tangent of \( \theta \):** The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. \[ \text{tan}(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \] \[ \text{tan}(\theta) = \frac{28.0 \, \text{m}}{21.0 \, \text{m}} \] \[ \text{tan}(\theta) = \frac{4}{3} \] **(c) Finding the sine of \( \varphi \):** The sine of an angle in a right triangle is the ratio of the length
Transcribed Image Text:**Title: Right Triangle Calculations** For the right triangle shown in the figure below, what are each of the following? (Let \( y = 28.0 \, \text{m} \) and \( r = 35.0 \, \text{m} \). Assume the triangle is a right triangle.) ![Right Triangle](image_link_here) **(a) The length of the unknown side (\( x \))** **(b) The tangent of \( \theta \)** **(c) The sine of \( \varphi \)** --- **Explanation of the Figure:** The diagram shows a right triangle with the hypotenuse \( r = 35.0 \, \text{m} \), one leg \( y = 28.0 \, \text{m} \), and an unknown leg \( x \). The angle opposite the leg \( y \) is labeled \( \theta \), and the angle opposite the unknown leg \( x \) is labeled \( \varphi \). **(a) Finding the length of the unknown side (\( x \)):** We use the Pythagorean Theorem which states: \[ r^2 = x^2 + y^2 \] Plugging in the given values: \[ 35.0^2 = x^2 + 28.0^2 \] \[ 1225 = x^2 + 784 \] Subtracting 784 from both sides: \[ 441 = x^2 \] Taking the square root of both sides: \[ x = \sqrt{441} \] \[ x = 21.0 \, \text{m} \] **(b) Finding the tangent of \( \theta \):** The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. \[ \text{tan}(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \] \[ \text{tan}(\theta) = \frac{28.0 \, \text{m}}{21.0 \, \text{m}} \] \[ \text{tan}(\theta) = \frac{4}{3} \] **(c) Finding the sine of \( \varphi \):** The sine of an angle in a right triangle is the ratio of the length
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