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.


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?

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  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.

    The first one:
    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 sin

    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 =
    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.

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