Question

given the right triangle shown below with one non-right angle of 44° and an adjacent side of length 11:
the measure of the other non-right angle is
and the lengths of the other sides are:
b ≈
c ≈
round your answers to one decimal place.
be sure to include the degree symbol in your answer for any angle measured in degrees.
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Explanation:

Step1: Find the other non - right angle

In a right triangle, the sum of the non - right angles is \(90^{\circ}\). Let the other non - right angle be \(x\). We know one non - right angle is \(44^{\circ}\), so \(x + 44^{\circ}=90^{\circ}\). Solving for \(x\), we get \(x = 90^{\circ}- 44^{\circ}=46^{\circ}\).

Step2: Find the length of side \(b\) (opposite to \(44^{\circ}\) angle)

We know that in a right triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 44^{\circ}\), adjacent side \(= 11\), and opposite side is \(b\). So \(\tan(44^{\circ})=\frac{b}{11}\). Then \(b = 11\times\tan(44^{\circ})\). Calculating \(\tan(44^{\circ})\approx0.9657\), so \(b\approx11\times0.9657\approx10.6\) (rounded to one decimal place).

Step3: Find the length of side \(c\) (hypotenuse)

We know that \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 44^{\circ}\), adjacent side \( = 11\), and hypotenuse is \(c\). So \(\cos(44^{\circ})=\frac{11}{c}\). Then \(c=\frac{11}{\cos(44^{\circ})}\). Calculating \(\cos(44^{\circ})\approx0.7193\), so \(c\approx\frac{11}{0.7193}\approx15.3\) (rounded to one decimal place).

Answer:

The measure of the other non - right angle is \(46^{\circ}\), \(b\approx10.6\), \(c\approx15.3\)