Question

Which of the following values best approximates of the length of c in triangle ABC where c = 90(degrees), b = 12, and B = 15(degrees)?

c = 3.1058
c = 12.4233
c = 44.7846
c = 46.3644

In triangle ABC, find b, to the nearest degree, given a = 7, b = 10, and C is a right angle.

35(degrees)
44(degrees)
46(degrees)
55(degrees)

Solve the right triangle ABC with right angle C if B = 30(degrees) and c = 10.

a = 5, b = 5, A = 60(degrees)
a = 5, b = 8.6602, A = 60(degrees)
a = 5.7735, b = 11.5470, A = 60(degrees)
a = 8.6602, b = 5, A = 60(degrees)

I'm horrible at trig and I do not know how to do this, please help?

Answer 1

"I am horrible at trig" is a cop-out.

All you have to remember in a right-angled triangle is 3 pairs of sides combinations for the primary trig functions.

Memorize the following word: SOH-CAH-TOA
SOH -- SinØ = Opposite/Hypotenuse , not the S,O, and H
CAH --CosØ = Adjacent/Hypotenus
TOA -- TanØ = Opposite/Hypotenuse

The other notation you should know that in labeling triangles, capital letters are usually used for the angles and small letters would be the sides opposite those angles.
Draw a right-angled triangle ABC, label it that way, and MEMORIZE the above, you are "horrible" at it only because you have not made the effort to learn this.

<b>The first one:</b>
Which of the following values best approximates of the length of c in triangle ABC where C = 90°, b = 12, and B = 15° ? (notice c ---> C, since C is an angle)

So in terms of the 15° angle , b is the Opposite and c is the Hypotenuse
so "opposite - hypotenuse" form SOH-CAH-TOA suggests <b>sin</b>

sin 15° = 12/c
c sin15 = 12
c = 12/sin15° = 46.3644

after doing a few, you can do each in 3 or less lines

#2, this time you are not given any angles, but you are given 2 sides
"In triangle ABC, find B, to the nearest degree, given a = 7, b = 10, and C is a right angle. " (notice I changed b --> B)

make your sketch , in terms of angle B, we are given the opposite and the adjacent, so that suggests tan
tanB = 10/7 = ....
B = 55° , see that? only 2 lines of actual work

(on my calculator, I did the following:
10÷7 =
2ndF
tan
=
and I got 55.0079.... )

try the rest, they are easy

by solving a triangle, you are finding all the missing sides and missing angles.
remember, in a right-angles triangle as soon as you have one of the smaller angle, you also have the third since their sum must be 90°
Also if you have 2 sides in a right-angled triangle you could also find the third by Pythagoras. This is often a good way to check your answers.