Here are the step-by-step solutions for each problem on the worksheet. We will use trigonometric ratios (Sine, Cosine, and Tangent) to find the missing sides. Remember SOH CAH TOA:
*
Sine =
Opposite /
Hypotenuse
*
Cosine =
Adjacent /
Hypotenuse
*
Tangent =
Opposite /
Adjacent
1) Find f
*
Identify sides: The angle is $55^\circ$. Side $f$ is Opposite. The hypotenuse is 40.
*
Choose ratio: Sine ($\sin = \text{Opp}/\text{Hyp}$).
*
Equation: $\sin(55^\circ) = \frac{f}{40}$
*
Solve: $f = 40 \times \sin(55^\circ)$
*
Calculate: $f \approx 40 \times 0.8192 = 32.768$
*
Round: $32.8$
2) Find y
*
Identify sides: The angle is $81^\circ$. Side $y$ is Opposite. The adjacent side is 24.
*
Choose ratio: Tangent ($\tan = \text{Opp}/\text{Adj}$).
*
Equation: $\tan(81^\circ) = \frac{y}{24}$
*
Solve: $y = 24 \times \tan(81^\circ)$
*
Calculate: $y \approx 24 \times 6.3138 = 151.53$
*
Round: $151.5$
3) Find o
*
Identify sides: The angle is $37^\circ$. Side $o$ is Opposite. The adjacent side is 12.
*
Choose ratio: Tangent ($\tan = \text{Opp}/\text{Adj}$).
*
Equation: $\tan(37^\circ) = \frac{o}{12}$
*
Solve: $o = 12 \times \tan(37^\circ)$
*
Calculate: $o \approx 12 \times 0.7536 = 9.04$
*
Round: $9.0$
4) Find o
*
Identify sides: The angle is $35^\circ$. Side $o$ is Adjacent. The opposite side is 24.
*
Choose ratio: Tangent ($\tan = \text{Opp}/\text{Adj}$).
*
Equation: $\tan(35^\circ) = \frac{24}{o}$
*
Solve: $o = \frac{24}{\tan(35^\circ)}$
*
Calculate: $o \approx \frac{24}{0.7002} = 34.27$
*
Round: $34.3$
5) Find j
*
Identify sides: The angle is $36^\circ$. Side $j$ is Adjacent. The hypotenuse is 45.
*
Choose ratio: Cosine ($\cos = \text{Adj}/\text{Hyp}$).
*
Equation: $\cos(36^\circ) = \frac{j}{45}$
*
Solve: $j = 45 \times \cos(36^\circ)$
*
Calculate: $j \approx 45 \times 0.8090 = 36.405$
*
Round: $36.4$
6) Find v
*
Identify sides: The angle is $34^\circ$. Side $v$ is Opposite. The hypotenuse is 37.
*
Choose ratio: Sine ($\sin = \text{Opp}/\text{Hyp}$).
*
Equation: $\sin(34^\circ) = \frac{v}{37}$
*
Solve: $v = 37 \times \sin(34^\circ)$
*
Calculate: $v \approx 37 \times 0.5592 = 20.69$
*
Round: $20.7$
7) Find v
*
Identify sides: The angle is $38^\circ$. Side $v$ is Adjacent. The hypotenuse is 45.
*
Choose ratio: Cosine ($\cos = \text{Adj}/\text{Hyp}$).
*
Equation: $\cos(38^\circ) = \frac{v}{45}$
*
Solve: $v = 45 \times \cos(38^\circ)$
*
Calculate: $v \approx 45 \times 0.7880 = 35.46$
*
Round: $35.5$
8) Find f
*
Identify sides: The angle is $48^\circ$. Side $f$ is Adjacent. The opposite side is 20.
*
Choose ratio: Tangent ($\tan = \text{Opp}/\text{Adj}$).
*
Equation: $\tan(48^\circ) = \frac{20}{f}$
*
Solve: $f = \frac{20}{\tan(48^\circ)}$
*
Calculate: $f \approx \frac{20}{1.1106} = 18.008$
*
Round: $18.0$
Final Answer:
1) 32.8
2) 151.5
3) 9.0
4) 34.3
5) 36.4
6) 20.7
7) 35.5
8) 18.0
Parent Tip: Review the logic above to help your child master the concept of sohcahtoa worksheet with answers.
