MATH SOLVE

6 months ago

Q:
# 4.1.4 practice: modeling: leaning towers.. Geometry Apex class...Can’t figure out how to do this

Accepted Solution

A:

Observe attached picture.

Letter a marks lean. Letter b marks height of leaned tower. Letter c marks length of side of tower.

a=7.4 feet

b=94 feet

c=?

From the picture we can see that we have right-angle triangle. We can use pythagorean theorem to solve for c.

[tex] a^{2} + b^{2} = c^{2} \\ \\ 7.4^{2} + 94^{2} = c^{2} \\ \\ c^{2} =8890.76 \\ \\ c=94.3feet[/tex]

We can use law of sines to solve for lean angle:

[tex] \frac{a}{sin \alpha } = \frac{b}{sin \beta }= \frac{c}{sin \gamma } [/tex]

We will use part:

[tex] \frac{b}{sin \beta }= \frac{c}{sin \gamma } \\ \\ c*sin \beta=b*sin \gamma \\ \\ sin \beta= \frac{b*sin \gamma}{c} \\ \\ sin \beta= \frac{94*sin \90}{94.3} \\ \\ sin \beta=0.99681866 \\ \\ \beta=85.4[/tex]

Tower makes angle of 85.4° with respect to ground or 4.6° with respect to vertical line.

Letter a marks lean. Letter b marks height of leaned tower. Letter c marks length of side of tower.

a=7.4 feet

b=94 feet

c=?

From the picture we can see that we have right-angle triangle. We can use pythagorean theorem to solve for c.

[tex] a^{2} + b^{2} = c^{2} \\ \\ 7.4^{2} + 94^{2} = c^{2} \\ \\ c^{2} =8890.76 \\ \\ c=94.3feet[/tex]

We can use law of sines to solve for lean angle:

[tex] \frac{a}{sin \alpha } = \frac{b}{sin \beta }= \frac{c}{sin \gamma } [/tex]

We will use part:

[tex] \frac{b}{sin \beta }= \frac{c}{sin \gamma } \\ \\ c*sin \beta=b*sin \gamma \\ \\ sin \beta= \frac{b*sin \gamma}{c} \\ \\ sin \beta= \frac{94*sin \90}{94.3} \\ \\ sin \beta=0.99681866 \\ \\ \beta=85.4[/tex]

Tower makes angle of 85.4° with respect to ground or 4.6° with respect to vertical line.