Question

HELP ME - I giv e 100 points

Answer 1

Given

• Triangles are 30°x60°x90° and 45°x45°

Use side ratios of each

• 45°x45° triangle a : b : c = 1 : 1 : √2
• 30°x60°x90° triangle a : b : c = 1 : √3 : 2

Question 18

• a = b = 12√2 ÷ √2 = 12
• c = a√3 = 12√3
• d = 2a = 2 × 12 = 24

Question 19

• a = 18√3 ÷ 2 = 9√3
• c = 18√3 ÷ √3 = 18
• d = a = 9√3
• b = a√2 = 9√3 × √2 = 9√6

Answer 2

Explanation:

we need to work out for b , c and d in both the triangles .

18.

we can use ratios of sine , cosine and tangent to find the required answers

i) finding a ,

sin45° = a/12√2

1/√2 = a/12√2

a = 12√2/√2

a = 12

ii)

cos45 = b/12√2

1/√2 = b/12√2

b = 12√2/√2

b = 12

iii)

tan 30 = a/c = 12/c

1/√3 = 12/c

c = 12√3

iv)

sin30 = a/d

1/2 = 12/d

d = 24

_______________________

19.

i)

sin60 = c/18√3

√3/2 = c/18√3

c = 18√3 * √3/2

c = 27

ii)

cos 60= a/18√3

1/2 = a/18√3

a = 1/2 * 18√3

a = 9√3

iii)

tan45 = a/d = 9√3/d

1 = 9√3/d

d = 9√3

iv)

sin45 = a/b = 9√3/b

1/√2 = 9√3/b

b = 9√3*√2

b = 9√6

and we are done!

-Rishabh