Question: If A= 29 degrees and a= 4.6, find c.
There is a diagram shown in the textbook. b is adjacent, c is the hypotenuse, and a is opposite. I know I'm suppose to use SOH CAH TOA, and i tried using tan, but Im not getting the correct answer. i looked in the back of the textbook to check my answer and it was incorrect. The correct answer is 9.5. The answer I got was 2.5. In my calculator I pressed tan and 29, then i times 4.6. I dont know what im doing wrong, please help.
Following your description I got
sin 29° = opp/hyp = 4.6/c
csin29 = 4.6
c = 4.6/sin29
= 9.48826.. or appr 9.5
I don't know how you got 2.5
To solve for the length of side c, we can use the trigonometric function of sine (SOH).
In this case, we have A = 29 degrees and a = 4.6, with c being the hypotenuse.
First, we need to find the measure of angle B, as it will help us determine which trigonometric function to use.
Since the sum of angles in a triangle is 180 degrees, angle B = 180 - 90 - 29 = 61 degrees.
Now we can use the sine function: sin(B) = opposite/hypotenuse.
sin(B) = a/c
sin(61) = 4.6/c
To find c, we rearrange the equation and solve for c:
c = 4.6 / sin(61)
Using a calculator, we find:
c = 4.6 / 0.870 = 5.287
Therefore, the length of side c is approximately 5.287, which is different from what you calculated.
It seems that there was an error in your calculation. Instead of using the tangent function, you should have used the sine function to solve for the length of c.
Please make sure to enter the values and functions correctly in your calculator to get the accurate result.
If you still have any further questions or need additional assistance, please let me know.
To solve this problem using the tangent function, you need to use the angle A and the length of the side a. However, there seems to be some confusion in the calculation you described. Let me explain how to correctly use the tangent function:
1. Start by identifying which sides and angles are given in the problem. In this case, angle A is given as 29 degrees, and the length of side a is given as 4.6.
2. Recall that in a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Mathematically, it can be represented as tan(A) = opposite/adjacent.
3. Substitute the given values into the formula: tan(29) = a/b. In this case, the opposite side is a, and the adjacent side is b.
4. Rearrange the formula to solve for c, the hypotenuse. c = a / tan(A).
5. Now, plug in the values: c = 4.6 / tan(29).
6. Use a calculator to find the tangent of 29 degrees: tan(29) ≈ 0.5543.
7. Finally, divide the length of side a by the tangent of 29 degrees: c = 4.6 / 0.5543 ≈ 8.29.
So, the correct answer for the length of the hypotenuse c is approximately 8.29, not 9.5. Therefore, it seems there might be an error in the back of your textbook.