We have been given that in ΔBCD, the measure of ∠D=90°, the measure of ∠C=42°, and CD = 7.5 feet. We are asked to find the length of DB to nearest tenth of foot.
First of all, we will draw a right triangle using our given information.
We can see from the attachment that DB is opposite side to angle C and CD is adjacent side to angle.
We know that tangent relates opposite side of right triangle to adjacent side of right triangle.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(\angle C)=\frac{DB}{CD}[/tex]
[tex]\text{tan}(42^{\circ})=\frac{DB}{7.5}[/tex]
[tex]7.5\cdot\text{tan}(42^{\circ})=\frac{DB}{7.5}\cdot 7.5[/tex]
[tex]7.5\cdot\text{tan}(42^{\circ})=DB[/tex]
[tex]7.5\cdot0.900404044298=DB[/tex]
[tex]DB=7.5\cdot0.900404044298[/tex]
[tex]DB=6.753030332235\approx 6.8[/tex]
Therefore, the length of DB is approximately 6.8 feet.
