Hi, Ashley.

For this problem, drawing a simple sketch of the situation helps. Choose a point to represent the boat, and draw a horizontal segment from the boat to the base of the cliff. Label the length of this segment as 991 feet. Now draw a vertical segment from the base of the cliff to the top of the cliff. Label the length of this segment h (for "height"). Finally, connect the point representing the boat with the point at the top of the cliff. The angle formed by this segment and the first segment you drew is the angle of elevation, so label its measure as 18°41'.

What you've drawn is a right triangle (because the intersection of a horizontal line and a vertical line forms a right angle). You know the length of the leg adjacent to the angle of elevation, and you want to find the length of the leg opposite the angle of elevation. The appropriate trig ratio to use in this case is tangent. (Remember that the tangent of an acute angle in a right triangle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle.)

So, write the equation tan(18°41') = h/991. Solving for h gives h = 991 tan(18°41'). You'll need to use a scientific calculator set in degree mode to find a decimal approximation of h. You'll also need to convert 41 minutes to degrees. Because there are 60 minutes in 1 degree, 41 minutes represents 41/60 degree, or about 0.68333 degree. So, use the calculator to find 991 tan(18.68333°). You'll get 335 rounded to the ones place. So, the height of the cliff is 335 feet to the nearest foot.

Doug