A computer is used to pick three letters, one after the other, from {A.B}. Each letter can be picked more than once and has the
2 answers:
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Answer:
16. Angle C is approximately 13.0 degrees.
17. The length of segment BC is approximately 45.0.
18. Angle B is approximately 26.0 degrees.
15. The length of segment DF "e" is approximately 12.9.
Step-by-step explanation:
<h3>16</h3>By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.
For triangle ABC:
,
- The opposite side of angle A
,
- The angle C is to be found, and
- The length of the side opposite to angle C
.
.
.
.
Note that the inverse sine function here is also known as arcsin.
By the law of cosine,
,
where
,
, and
are the lengths of sides of triangle ABC, and
is the cosine of angle C.
For triangle ABC:
,
,
- The length of
- The cosine of angle A is
.
Therefore, replace C in the equation with A, and the law of cosine will become:
.
.
For triangle ABC:
,
,
, and
- Angle B is to be found.
Start by finding the cosine of angle B. Apply the law of cosine.
.
.
.
For triangle DEF:
- The length of segment DF is to be found,
- The length of segment EF is 9,
- The sine of angle E is
, and
- The sine of angle D is
.
Apply the law of sine:
.
