Rectangular box has a horizontal base EFGH where HG = 15 cm,GF =8cm and BF=7cm. X is a point on AB such that XB=4cm. Calculate the angle CEG and GXF.
Please calculate e in the angle CEG and X IN GXF
First, the rectangular base EFGH is parallel to the rectangular top ABCD, therefore AB=EF=GH = 15cm.
Since the lateral sides are also rectangles, therefore BF is parallel to CG => BF = CG = 7cm.
The triangle CGE is a right angled and the angle G measures 90 degrees.
To calculate the included angle CEG, we'll calculate the length of the side EG, using the right angled triangle EFG, where EG is the hypotenuse.
EG = `sqrt(15^2 + 8^2)`
EG = `sqrt(289)`
EG = 17
We'll keep only the positive result, since a length of aide cannot be negative.
We'll return to the right angle triangle CEG, where EG and CG are the legs of triangle. To determine the measure of the angle CEG, we'll use tangent function:
tan CEG = CG/EG
tan CEG = 7/17
tan CEG = 0.4117
CEG = 22.37 degrees
To calculate the measure of GXF, we need to determine the length of FX and GX.
The length of GX can be determine from the right angle triangle GCX. We need first to determine CX, from the top right angle triangle CBX.
CX = `sqrt(4^2 + 8^2)`
CX = `sqrt(80)`
CX = 4`sqrt(5)`
Now, we'll determine XG, from the right angle triangle GCX:
GX = `sqrt(80+49)`
GX = `sqrt(129)`
We'll determine the length of FX from the triangle FBX.
FX = `sqrt(16+49)`
FX = `sqrt(65)`
We'll use the law of cosine to determine the measure of GXF:
FG^2 = FX^2 + GX^2 - 2FX*GX*cos GXF
64 = 65 + 129 - 2*65*129*cosGXF
-130 = -16770*cosGXF
cosGXF = 130/16770
cosGXF = 0.00775
GXF = 89.55 degrees
Therefore, the angle CEG measures 22.37 degrees and the angle GXF measures 89.55 degrees.
The answer for GXF is 44.8 so do we have to divide 89.55 by 2 to get the answer.