Answer:
BC ≈ 4.0
Step-by-step explanation:
∠ DCA = 180° - 70° = 110° ( adjacent angles )
∠ DAC = 180° - (30 + 110)° ← sum of angles in triangle
∠ DAC = 180° - 140° = 40°
Using the Sine rule in Δ ACD to find common side AC
=
( cross- multiply )
AC × sin40° = 15 × sin30° ( divide both sides by sin40° )
AC = ≈ 11.668
Using the cosine ratio in right triangle ABC
cos70° = =
=
( multiply both sides by 11.668 )
11.668 × cos70° = BC , then
BC ≈ 4.0 ( to the nearest tenth )
By using trigonometric relations, we will see that:
AC = 15.6 in
AB = 8.4 in.
<h3>How to get the measures of the other two sides of the right triangle?</h3>Here we have the right triangle where:
B = 90°
C = 40°
BC = 10 in.
Notice that is the adjacent cathetus to the angle C, then we can use the two relations:
Where:
Then we will have:
sin(40°) = 10in/AC.
AC = 10in/sin(40°) = 15.6 in
tan(40°) = AB/10in
tan(40°)*10in = AB = 8.4 in.
So we can conclude that for the given right triangle we have:
AC = 15.6 in
AB = 8.4 in.
If you want to learn more about right triangles:
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