Answer:
Step-by-step explanation:
Picture 1
In right triangle ABC,
Side AB is the opposite side of angle C.
Picture 2
In triangle MKL,
tan(∠M) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{KL}{KM}[/tex]
= [tex]\frac{15}{8}[/tex]
Option (1) is the answer.
Picture 3
In ΔXYZ,
sin(∠Z) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{XY}{XZ}[/tex]
For the length of XY we will apply Pythagoras theorem in ΔXYZ,
XZ² = XY² + YZ²
XY² = XZ² - YZ²
= (40)² - (32)²
XY = √576
= 24
sin(Z) = [tex]\frac{24}{40}[/tex]
sin(Z) = [tex]\frac{3}{5}[/tex]
Picture 4
In right triangle DEF,
Cos(D) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{EF}{DF}[/tex]
= [tex]\frac{75}{72}[/tex]
= [tex]\frac{25}{24}[/tex]
Picture 5
In ΔABC,
tan(63°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(63°) = [tex]\frac{BC}{AB}[/tex]
AB = [tex]\frac{BC}{\text{tan}(63)}[/tex]
AB = [tex]\frac{8}{\text{tan}(63)}[/tex]
AB = 4.0762 ≈ 4 m
Option (3) will be the answer.
