Trigonometry Examples

$95 ° 3' 55''$

Step 1

Since $95$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $3$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $55$ by $\frac{1}{3600}$ . Add them together.

$95 + 3 \cdot \frac{1}{60} + 55 \cdot \frac{1}{3600}$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Remove parentheses.

$95 + 3 \cdot \frac{1}{60} + 55 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1

Factor $3$ out of $60$ .

$95 + 3 \cdot \frac{1}{3 (20)} + 55 \cdot \frac{1}{3600}$

Step 2.2.1.2

Cancel the common factor.

$95 + 3 \cdot \frac{1}{3 \cdot 20} + 55 \cdot \frac{1}{3600}$

Step 2.2.1.3

Rewrite the expression.

$95 + \frac{1}{20} + 55 \cdot \frac{1}{3600}$

Step 2.2.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.2.1

Factor $5$ out of $55$ .

$95 + \frac{1}{20} + 5 (11) \cdot \frac{1}{3600}$

Step 2.2.2.2

Factor $5$ out of $3600$ .

$95 + \frac{1}{20} + 5 \cdot 11 \cdot \frac{1}{5 \cdot 720}$

Step 2.2.2.3

Cancel the common factor.

$95 + \frac{1}{20} + 5 \cdot 11 \cdot \frac{1}{5 \cdot 720}$

Step 2.2.2.4

Rewrite the expression.

$95 + \frac{1}{20} + 11 \cdot \frac{1}{720}$

Step 2.2.3

Combine $11$ and $\frac{1}{720}$ .

$95 + \frac{1}{20} + \frac{11}{720}$

Step 2.3

Find the common denominator.

Tap for more steps...

Step 2.3.1

Write $95$ as a fraction with denominator $1$ .

$\frac{95}{1} + \frac{1}{20} + \frac{11}{720}$

Step 2.3.2

Multiply $\frac{95}{1}$ by $\frac{720}{720}$ .

$\frac{95}{1} \cdot \frac{720}{720} + \frac{1}{20} + \frac{11}{720}$

Step 2.3.3

Multiply $\frac{95}{1}$ by $\frac{720}{720}$ .

$\frac{95 \cdot 720}{720} + \frac{1}{20} + \frac{11}{720}$

Step 2.3.4

Multiply $\frac{1}{20}$ by $\frac{36}{36}$ .

$\frac{95 \cdot 720}{720} + \frac{1}{20} \cdot \frac{36}{36} + \frac{11}{720}$

Step 2.3.5

Multiply $\frac{1}{20}$ by $\frac{36}{36}$ .

$\frac{95 \cdot 720}{720} + \frac{36}{20 \cdot 36} + \frac{11}{720}$

Step 2.3.6

Multiply $20$ by $36$ .

$\frac{95 \cdot 720}{720} + \frac{36}{720} + \frac{11}{720}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{95 \cdot 720 + 36 + 11}{720}$

Step 2.5

Simplify the expression.

Tap for more steps...

Step 2.5.1

Multiply $95$ by $720$ .

$\frac{68400 + 36 + 11}{720}$

Step 2.5.2

Add $68400$ and $36$ .

$\frac{68436 + 11}{720}$

Step 2.5.3

Add $68436$ and $11$ .

$\frac{68447}{720}$

Step 3

Convert the fraction to a decimal by dividing the numerator by the denominator.

$95.0652\overline{7} °$