Question

question: 5
a 32 flat screen television measures 32
inches across its diagonal. the diagonal
makes a 35 angle with the bottom of the
television.
select all equations that can be used to solve
for the height, h, of the television screen.
□ a. cos35°=\\( \frac { h } { 32 } \\)
□ b. sin35°=\\( \frac { h } { 32 } \\)
□ c. tan35°=\\( \frac { h } { 32 } \\)
□ d. cos55°=\\( \frac { h } { 32 } \\)
□ e. sin55°=\\( \frac { h } { 32 } \\)
□ f. tan55°=\\( \frac { h } { 32 } \\)

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the hypotenuse is the diagonal of the television (\(32\) inches), and the height \(h\) is the side opposite to the \(35^{\circ}\) angle.

Step2: Analyze each option

• Option A: \(\cos35^{\circ}=\frac{\text{adjacent}}{\text{hypotenuse}}\). The adjacent side to the \(35^{\circ}\) angle is not \(h\), so \(\cos35^{\circ}

eq\frac{h}{32}\).

• Option B: \(\sin35^{\circ}=\frac{\text{opposite}}{\text{hypotenuse}}\). Since \(h\) is the side opposite to the \(35^{\circ}\) angle and the hypotenuse is \(32\), \(\sin35^{\circ}=\frac{h}{32}\).
• Option C: \(\tan35^{\circ}=\frac{\text{opposite}}{\text{adjacent}}\). The adjacent side to the \(35^{\circ}\) angle is not \(32\), so \(\tan35^{\circ}

eq\frac{h}{32}\).

• Option D: Since \(90^{\circ}-35^{\circ} = 55^{\circ}\), \(\cos55^{\circ}=\cos(90^{\circ}-35^{\circ})=\sin35^{\circ}\). And \(\sin35^{\circ}=\frac{h}{32}\), so \(\cos55^{\circ}=\frac{h}{32}\).
• Option E: \(\sin55^{\circ}=\sin(90^{\circ}-35^{\circ})=\cos35^{\circ}\). The adjacent side to the \(35^{\circ}\) angle is not \(h\), so \(\sin55^{\circ}

eq\frac{h}{32}\).

• Option F: \(\tan55^{\circ}=\frac{\text{opposite}}{\text{adjacent}}\). The adjacent side to the \(55^{\circ}\) angle is not \(32\), so \(\tan55^{\circ}

eq\frac{h}{32}\).

Answer:

B. \(\sin35^{\circ}=\frac{h}{32}\), D. \(\cos55^{\circ}=\frac{h}{32}\)