Kuta Software – Infinite Algebra 1 Using Trigonometry To Find Lengths Find the missing side. Round to the nearest tenth. 1) 27° 10 2)
The Correct Answer and Explanation is:
To solve for the missing side in a right triangle using trigonometry, we typically use one of the following trigonometric functions:
- Sine (sin): sin(θ)=oppositehypotenuse\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}sin(θ)=hypotenuseopposite
- Cosine (cos): cos(θ)=adjacenthypotenuse\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}cos(θ)=hypotenuseadjacent
- Tangent (tan): tan(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}tan(θ)=adjacentopposite
For question 1:
Given:
- Angle θ=27∘\theta = 27^\circθ=27∘
- One side is given as 10 (you didn’t specify whether it’s adjacent, opposite, or hypotenuse, so I’ll provide an explanation assuming the missing side is the opposite or adjacent).
Assume the given side is the adjacent side, and we need to find the opposite side. We can use the tangent function:tan(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}tan(θ)=adjacentopposite
Substitute the known values:tan(27∘)=opposite10\tan(27^\circ) = \frac{\text{opposite}}{10}tan(27∘)=10opposite
Now, solve for the opposite side:opposite=10⋅tan(27∘)\text{opposite} = 10 \cdot \tan(27^\circ)opposite=10⋅tan(27∘)opposite≈10⋅0.5095\text{opposite} \approx 10 \cdot 0.5095opposite≈10⋅0.5095opposite≈5.1\text{opposite} \approx 5.1opposite≈5.1
Thus, the missing side (opposite) is approximately 5.1.
For question 2:
If you have a specific angle or side for question 2, feel free to provide it, and I can calculate the missing side accordingly!
