Question

Find x. A. 21√2 B. 7 C. 21√3 over 2 D. 21√2 over 2

Answer 1

Answer:

D

Step-by-step explanation:

for you to find x you first have to find the adjacent of the 45° angle you can do that by using the other triangle.using the sin ratio

sin60=opposite/hypotenuse

sin60=a/7√3

a=10.5

then after you have found the adjacent you can use the cos ratio

cos45=adjacent/hypotenuse

cos45=10.5/x

cos45x/cos45=10.5/cos45

x=14.849

which is the same as 21√2 over 2

I hope this helps

Answer 2

Answer:

D

Step-by-step explanation:

Using sine ratio in left right angled triangle to find the altitude a of the large triangle which is common to both right triangles and the exact value

sin60° = $\frac{\sqrt{3} }{2}$ , then

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{a}{7\sqrt{3} }$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2a = 21 ( divide both sides by 2 )

a = $\frac{21}{2}$

Using the cosine ratio in the right side triangle and the exact value

cos45° = $\frac{1}{\sqrt{2} }$ , then

cos45° = $\frac{adjacent}{hypotenuse}$ = $\frac{a}{x}$ = $\frac{1}{\sqrt{2} }$ ( cross- multiply )

x = $\sqrt{2}$ a = $\sqrt{2}$ × $\frac{21}{2}$ = $\frac{21\sqrt{2} }{2}$ → D