Question

9. Nick has desigied a diamond-shaped kite as shown below. The measures of so me sides of the kite, are marked in the

figure. Find the value of x (JUSTIFY)

Answer 1

`x=(10√(6))/(7)\ in`

Explanation:

step 1

In the right triangle DOC

Find the measure of side DO

Applying the Pythagoras Theorem

`DC^(2)=DO^(2)+OC^(2)`

substitute the given values

`7^(2)=DO^(2)+5^(2)`

`DO^(2)=7^(2)-5^(2)`

`DO^(2)=49-25`

`DO^(2)=24`

`DO=2√(6)\ in`

step 2

In the right triangle DOC

Find the sine of angle ∠ODC

sin(∠ODC)=OC/DC

substitute

`sin(ODC)=5/7` -----> equation A

step 3

In the right triangle DOP

Find the sine of angle ∠ODP

sin(∠ODP)=OP/DO

substitute

`sin(ODP)=x/2√(6)` -----> equation B

step 4

Find the value of x

In this problem

∠ODC=∠ODP

so

equate equation A and equation B

`5/7=x/2√(6)`

`x=(10√(6))/(7)\ in`