Find the missing side. Approximate the answer to three decimal places when appropriate.
Possible answers are: (A) 10yd, (B)31.623yd, (C) 20yd, (D) 400yd. Can you help me? I have done this so far. 180-15-25=140. I have tried everything that I know of to get the answer but I'm ata loss. I have tried the examples for this question but I'm not coming up with anything.
You'd better describe the figure if you want some help.
This is a triangle with sides of A,B,C.
Side A = 15 yd and side C=25 yd. I need to find the missing side
any side is less than the sum of the other two sides, so the missing side must be less than 40.
That eliminates (D)
Other than that, we need more information. Imagine you have two sticks of length 15 and 25. Connect one end of each together, into a V shape.
Now, you can imagine that you can wave the sticks about, making the 3rd side anything between 0 and 40 yd.
Still need one more piece of info, like an angle. If the angle between the two sides is a right angle, then the third side is √(15^2+25^2) = √850 = 29.15, so that's not it.
What else do you know?
Oh, yeah. The 3rd side must be greater than 10, since 25 < 15+x. So (A) is out.
That leaves (B) and (C) as possibilities.
To find the missing side, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
The Law of Cosines is given by the formula:
c² = a² + b² - 2ab * cos(C)
where c is the side opposite angle C, and a and b are the other two sides.
In this case, we have:
c = unknown side (which we are trying to find)
a = 15yd (given)
b = 25yd (given)
C = 180 - 15 - 25 = 140 degrees (as you correctly calculated)
Now we can plug in these values into the Law of Cosines equation:
c² = 15² + 25² - 2 * 15 * 25 * cos(140)
Calculating this equation:
c² ≈ 225 + 625 - 750 * cos(140)
To evaluate cos(140), you can use a scientific calculator or an online trigonometric calculator. Once you have the value of cos(140), you can substitute it back into the equation to find c².
Finally, take the square root to find c, the missing side. Approximate your answer to three decimal places, as requested.
Compare your calculated value of c with the given answers, (A) 10yd, (B)31.623yd, (C) 20yd, (D) 400yd, and choose the option that matches your calculated value most closely.