Find the area of each triangle. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.

Accepted Solution

First, it is important to remember that the formula to calculate the area of a triangle is: A=bxh/2 As we can see in the exercises, all the triangles are divided in two triangles. So, let's call "a" to the triangle on the left and "b" to the triangle on the right.
 9)To find the area of the triangle "a", we need the lenght of the adjacent leg (x) and the opposite leg (ya): Cos(α)=adjacent leg/hypotenuse  Cos(63°)=x/35 x=35xCos(63°) x=15.9  Sin(α)=opposite leg/hypotenuse
 Sin(63°)=ya/35 ya=35xSin(63°) ya=31.2
 Area(a)= (15.9x31.2)/2 Area(a)=248.0   Now, we proceed to find the area of "b". We already have the length x=15.9, so:  Tan(α)=opposite leg/adjacent leg yb=15.90xTan(42°) yb=14.3
 Area(b)=15.9X14.3/2 Area(b)=113.7
 The total Area (At) is:  At=Area(a)+Area(b) At=248.0+113.7 At=361.7
 10) Triangle "a": -Adjacent leg of the triangle "a": Cos(α)=adjacent leg/hypotenuse  Cos(30°)=xa/48 xa=48xCos(30°)  xa=41.6
 -Opposite leg of the triangle "a": Sin(α)=opposite leg/hypotenuse Sin(30°)=y/48 y=48xSin(30°) y=24.0
 -Area of the triangle "a": Area(a)=41.6x24.0/2 Area(a)=499.2
 Triangle "b": -We have the value of i(y=24).
 -Adjacent leg of the triangle "b": Tan(α)=opposite leg/adjacent leg Tan(45°)=24/xb xb=24/Tan(45°) xb=24
 -Area of the triangle "b": Area(b)= 24x24/2 Area(b)=288
 -Total area of the triangle (At) is: At=Area(a)+Area(b) At=499.2+288 At=787.2
 11) To find the area of the triangle shown in this exercise, we have to apply the same procedure as in exercise 10: -Adjacent leg of the triangle "a": Cos(α) = adjacent leg/hypotenuse  Cos(56°)=xa/14 xa=14xCos(56°) xa=7.8
 -Opposite leg of the triangle "a": Sin(α)=opposite leg/hypotenuse Sin(56°)=y/14 y=14xSin(56°) y=11.6
 -Area of the triangle "a": Area(a)=7.8x11.6/2 Area(a)=45.2
 Triangle "b": -The value of its opposite leg is y=11.6.
 -Adjacent leg of the triangle "b": Tan(α)=opposite leg/adjacent leg Tan(46°)=11.6/xb xb=11.6/Tan(46°) xb=11.2
 -Area of the triangle "b": Area(b)= 11.6x11.2/2 Area(b)=65.0
 -Total area of the triangle (At) is: At=Area(a)+Area(b) At=45.2+65.0 At=110.2
 12)-Adjacent leg of the triangle "a": Cos(α)=adjacent leg/hypotenuse  Cos(54°)=xa/13 xa=13xCos(54°) xa=7.6
 -Opposite leg of the triangle "a": Sin(α)=opposite leg/hypotenuse Sin(54°)=y/13 y=13xSin(54°) y=10.5
 -Area of the triangle "a": Area(a)=7.6x10.5/2 Area(a)=39.9
 Triangle "b": -Adjacent leg of the triangle "b": Tan(α)=opposite leg/adjacent leg Tan(42°)=7.6/xb xb=7.6/Tan(42°) xb=8.4
 -Area of the triangle "b": Area(b)=7.6x8.4/2 Area(b)=31.9
 -Total area of the triangle (At) is: At=Area(a)+Area(b) At=39.9+31.9 At=71.8