Question

Help with PreCal/Trig Please.

a.What is the length of the hypotenuse of triangle ABC?

b.What is the length of the shorter leg of triangle ABC?

c.What is the length of the longer leg of triangle ABC?

Answer 1

so can you find all your angles?? And what are your trig rules? SOHCAHTOA, right?

Answer 2

And you have a right triangle...

Answer 3

looks like similar triangles to me, what do you think?

Answer 4

I'm going to answer these questions independently and not in the order they were posed if you don't mind.

First off, we can completely characterize (find all the lengths of) the larger triangle ABC using the two smaller triangles formed by the perpendicular bisector of AB.

b. Evaluating the smaller triangle to the left of the perpendicular bisector of AB, using the definition of sine, we have that: sin(60) = side opposite of angle/hypotenuse. This can be written as sin(60) = 10/AC. Manipulating this algebraic equation and solving for AC will give you the length of the shorter leg of the larger triangle ABC.
this is the answer to part b.

c. We use a similar approach for the length of the larger leg of ABC. By evaluating the larger triangle (the right one) formed by the perpendicular bisector of AB, using the definition of sine again we have that sin(30) = side opposite of angle/hypotenuse, which in this case will be sin(30) = 10/BC. Manipulating this algebraic equation and solving for BC will give you the length of the longer leg of the larger triangle ABC.
this is the answer to part c.

a. Since the triangle ABC is a right triangle, knowing the lengths of AC and BC (the two legs of the triangle ABC) we can use the Pythagorean Theorem to solve for the hypotenuse of ABC. so AC^2 + BC^2 = AB^2.

Answer 5

the evaluations should be pretty straight forward. sin(A) = a/h. to solve for h, we first evaluate sin(A) since we know what A is so let's say sin(A) = .5. Then we have .5 = a/h, we then multiply both sides of the equation by h, so h*(.5)= a, and since we are solving for h and we know what a is, we isolate h by dividing both sides by .5 and we obtain that h = a/(.5) or equivalently h = 2(a)

Answer 6

*straightforward

Answer 7

Thank you so much!