Question

To find the distance between a point X and an inaccessible point​ Z, a line segment XY is constructed. Measurements show that XYequals946 ​m, angle XYZequals12 degrees 36 prime​, and angle YZXequals99 degrees 42 prime. Find the distance between X and Z to the nearest meter.

Answer 1

`XZ=209\ m`

Explanation:

step 1

Convert degrees and minutes to degrees

Remember that

`1^o=60'`

so

`m\angle XYZ=12^o36'=12^o+(36/60)=12.6^o`

`m\angle YZX=99^o42'=99^o+(42/60)=99.7^o`

step 2

Applying the law of sines

`(XY)/(sin(YZX))=(XZ)/(sin(XYZ))`

substitute the given values

`(946)/(sin(99.7^o))=(XZ)/(sin(12.6^o))`

solve for XZ

`XZ=(946)/(sin(99.7^o))sin(12.6^o)=209\ m`