Mathematics
xjezzer:

can someone help me with this trig problem

xjezzer:

Vocaloid:

I'll use E for J(e)nna and O for J(o)celyn At the start, they're both standing 50m apart, looking at the tree. Jenna's angle of elevation to the tree is 41 degrees. Jocelyn's is 52 degrees. We can illustrate the situation like so: |dw:1653617551011:dw|

Vocaloid:

let's say Jocelyn is standing some distance (x) from the base of the hill. Since Jocelyn and Jenna are standing 50m apart, Jenna must be 50-x meters away from the hill. Let's also call the height of the hill y. |dw:1653617734355:dw|

Vocaloid:

now we can set up two tan ratios (opposite/adjacent), one for each person Jocelyn: tan(theta) = opposite/adjacent tan(52) = y/x Jenna: tan(41) = y/(50-x) you have a system of two equations. solve for x and y.

Vocaloid:

once you have the x and y values, consider Jocelyn again. When she looks at the top of the tree, the new angle is 54. |dw:1653617880937:dw| set up another tan ratio, one for when she's looking at the bottom of the tree, and another when she's looking at the top of the tree. at the bottom of the tree: tan(52) = y/x at the top of the tree: tan(54) = (y+h)/x where h is the height of the tree. solve for the height of the tree. now, the tree needs to be more than 5 feet long to make the boat. so simply report whether the height of the tree is at least 5 or not based on your calculation, and whether they can build the boat.