Question

How do you solve for the unknown lengths and angle measures of triangle ABC where angle C = 90 degrees, angle B = 23 degrees and side a = 24?

Answer 1

`A=90^circ-B=67^circ`

`b = a tan B approx 10.19`

`c = a/cos B approx 26.07`

Explanation:

We have a right triangle, `a=24, C=90^circ, B=23^circ.`

The non-right angles in a right triangle are complementary,

`A=90^circ-23^circ=67^circ`

In a right triangle we have

`cos B = a/c`

`tan B = b/a`

so

`b = a tan B = 24 tan 23 approx 10.19`

`c = = a/cos B = 24/cos 23 approx 26.07`

Answer 2

Refer explanation.

Explanation:

Your question indicates unknown lengths which means you want to find length of `b` and `c` i assume.

Provided information : Angle B at `23` degrees // Length of `a` = `24` cm

To find length of `c`, use the provided info :

`sin (23) = c/24`

`:. c = 9.38cm` (Rounded off)

When `2` lengths are found, to find `b` apply Pythagoras Theorem

`sqrt (24^2 - 9.38^2)` = `22.09` cm (`b`)

To check if our values correspond to the angle given,

`tan^-1(9.28/22.09) = 23` degrees `sqrt`

Since triangle = `180` degrees, to find angle `A`,

`180 - 23 - 90 = 57` degrees

Answer 3

`angle A=67^@,b=10.187,c=26.072`

Explanation:

`:.180-(90+23)=67^@`

`:.(opposite)/(adjacent)=tan 23^@`

`:.opposite=adjacent xx tan 23^`

`:.opposite=24 xx tan 23`

`:.opposite=10.187=b`

Pythagoras:-

`:.c^2=a^2+b^2`

`:.c^2=24^2+10.187^2`

`:.c^2=576+103.775`

`:.c^2=679.775`

`:.sqrt(c^2)=sqrt(679.775)`

`:.c=26.072`