What is the general solution for ((176)^2)/(300*32.2)=tan(θ+30.9637) ?

The general solution for ((176)^2)/(300*32.2)=tan(θ+30.9637) is θ=1.26849…+180n-30.96370…

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Popular >

((176)^2)/(300*32.2)=tan(θ+30.9637)

Solution

\frac{( 176 ) ^{2}}{300 \cdot 32.2} = tan (θ + 30.963 7^{\circ})

Solution

θ = 1.26849 \dots + 18 0^{\circ} n - 30.96370 \dots^{\circ}

Radians

θ = 1.26849 \dots - \frac{1071 π}{6226} + πn

Solution steps

\frac{( 176 ) ^{2}}{300 \cdot 32.2} = tan (θ + 30.963 7^{\circ})

Switch sides

tan (θ + 30.96370 \dots^{\circ}) = \frac{17 6 ^{2}}{300 \cdot 32.2}

Simplify

\frac{17 6 ^{2}}{300 \cdot 32.2} : \frac{7744}{2415}

\frac{17 6 ^{2}}{300 \cdot 32.2}

Multiply the numbers:

300 \cdot 32.2 = 9660

= \frac{17 6 ^{2}}{9660}

Factor

17 6^{2} : 2^{8} \cdot 1 1^{2}

Factor

176 = 2^{4} \cdot 11

= (2^{4} \cdot 11)^{2}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

= 1 1^{2} (2^{4})^{2}

Simplify

(2^{4})^{2} : 2^{8}

(2^{4})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 2^{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= 2^{8}

= 2^{8} \cdot 1 1^{2}

Factor

9660 : 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 23

Factor

9660 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 23

= \frac{2 ^{8} \cdot 1 1 ^{2}}{2 ^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 23}

Cancel

\frac{2 ^{8} \cdot 1 1 ^{2}}{2 ^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 23} : \frac{2 ^{6} \cdot 1 1 ^{2}}{3 \cdot 5 \cdot 7 \cdot 23}

\frac{2 ^{8} \cdot 1 1 ^{2}}{2 ^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 23}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{8}}{2 ^{2}} = 2^{8 - 2}

= \frac{1 1 ^{2} \cdot 2 ^{8 - 2}}{3 \cdot 5 \cdot 7 \cdot 23}

Subtract the numbers:

8 - 2 = 6

= \frac{2 ^{6} \cdot 1 1 ^{2}}{3 \cdot 5 \cdot 7 \cdot 23}

= \frac{2 ^{6} \cdot 1 1 ^{2}}{3 \cdot 5 \cdot 7 \cdot 23}

Multiply the numbers:

3 \cdot 5 \cdot 7 \cdot 23 = 2415

= \frac{2 ^{6} \cdot 1 1 ^{2}}{2415}

2^{6} \cdot 1 1^{2} = 7744

2^{6} \cdot 1 1^{2}

2^{6} = 64

= 1 1^{2} \cdot 64

1 1^{2} = 121

= 64 \cdot 121

Multiply the numbers:

64 \cdot 121 = 7744

= 7744

= \frac{7744}{2415}

Apply trig inverse properties

tan (θ + 30.96370 \dots^{\circ}) = \frac{7744}{2415}

General solutions for

tan (θ + 30.96370 \dots^{\circ}) = \frac{7744}{2415}

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

θ + 30.96370 \dots^{\circ} = arctan (\frac{7744}{2415}) + 18 0^{\circ} n

θ + 30.96370 \dots^{\circ} = arctan (\frac{7744}{2415}) + 18 0^{\circ} n

Solve

θ + 30.96370 \dots^{\circ} = arctan (\frac{7744}{2415}) + 18 0^{\circ} n : θ = arctan (\frac{7744}{2415}) + 18 0^{\circ} n - 30.96370 \dots^{\circ}

θ + 30.96370 \dots^{\circ} = arctan (\frac{7744}{2415}) + 18 0^{\circ} n

Move

30.96370 \dots^{\circ}

to the right side

θ + 30.96370 \dots^{\circ} = arctan (\frac{7744}{2415}) + 18 0^{\circ} n

Subtract

30.96370 \dots^{\circ}

from both sides

θ + 30.96370 \dots^{\circ} - 30.96370 \dots^{\circ} = arctan (\frac{7744}{2415}) + 18 0^{\circ} n - 30.96370 \dots^{\circ}

Simplify

θ = arctan (\frac{7744}{2415}) + 18 0^{\circ} n - 30.96370 \dots^{\circ}

θ = arctan (\frac{7744}{2415}) + 18 0^{\circ} n - 30.96370 \dots^{\circ}

θ = arctan (\frac{7744}{2415}) + 18 0^{\circ} n - 30.96370 \dots^{\circ}

Show solutions in decimal form

θ = 1.26849 \dots + 18 0^{\circ} n - 30.96370 \dots^{\circ}

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Frequently Asked Questions (FAQ)

What is the general solution for ((176)^2)/(300*32.2)=tan(θ+30.9637) ?
The general solution for ((176)^2)/(300*32.2)=tan(θ+30.9637) is θ=1.26849…+180n-30.96370…