# Mr. Clark is finding his distance to a dock. He makes a turn of 90 degrees, measures 45 meters,and finds the acute angle to be 80 degrees.please write an equation that shows about how far he is...

Mr. Clark is finding his distance to a dock. He makes a turn of 90 degrees, measures 45 meters,and finds the acute angle to be 80 degrees.

please write an equation that shows about how far he is from the dock.then,solve the equation to find his distance from the dock. round to the nearest whole number.<it says that using trigonometric ratio table would be easier when solving>

thank you

james0tucson | (Level 2) Adjunct Educator

Posted on

If one leg of a right triangle is 45 meters, and one angle is 80 degrees, then the other angle is 10 degrees.  The unknown leg is 45 * tan(10).

It is unclear from the question whether we want to know his original distance (7.93 meters) or his new distance (the hypotenuse, 45.69 meters).

revolution | College Teacher | (Level 1) Valedictorian

Posted on

You need to use trigonmentry to solve this equation. Remember all the tangent, cosine and sine rule? Just make use all the lengths and the angles provided. Let see, he makes a turn of 90, and measures a leg of a triangle to be 45m. The acute angle is 80 degrees so the other angle should be 10 degree. Use the tangent rule to find one leg of the triangle. 45*tan10= 7.93m. That's the earlier distance from the dock.

If you are trying to find the new dist, not the original one, you should use the cosine rule, by using cos?= adjacent/hypotenuse. The answer should be around 45.6, to one decimal place.