Answer:
h = 28, x = 33
Step-by-step explanation:
First step:
use sine:
[tex]sine=\dfrac{opposite}{hypotenuse}[/tex]
We have:
[tex]m\angle A=39^o,\ hypotenuse=45,\ opposite=h[/tex]
[tex]\sin39^o\approx0.6293[/tex]
Substitute:
[tex]\dfrac{h}{45}=0.6293[/tex] multiply both sides by 45
[tex]h=28.3185\to h\approx28[/tex]
Second step:
Use tangent:
[tex]tangent=\dfrac{opposite}{adjacent}[/tex]
We have:
[tex]m\angle BDC=40^o,\ opposite=28,\ adjacent=x[/tex]
[tex]\tan40^o\approx0.8391[/tex]
Substitute:
[tex]\dfrac{28}{x}=0.8391[/tex]
[tex]\dfrac{28}{x}=\dfrac{8391}{10000}[/tex] cross multiply
[tex]8391x=280000[/tex] divide both sides by 8391
[tex]x\approx33.3691\to x\approx33[/tex]
