# How To Find A Tangent Angle

**How To Find A Tangent Angle** – 3 Example 1 Find Ratios of Tangents Find tan S and tan R. Write each answer as a fraction and a decimal, rounded to four digits. SOLUTION = opp S adj. S = RTST = 80 18 = 40 9 tan S 4.4444 = opp R adj. R = STRT = 18 80 = 9 40 tan R 0.2250 =

4 Guided Practice Example 1 Find tan J and tan K. Round to four decimal places. 0.7500 answer, 0.5333 answer,

## How To Find A Tangent Angle

Example 2 Find the length of a leg Algebra Find the value of x. Solution Use the tangent of an acute angle to find the length of the leg. tan 32o = opp. adj. Write the ratio of the tangent of 32o. tan 32o 11 = x Substitute. x tan 32o = 11 Multiply each side by x. x = 11 tan 32o Divide each side by tan 32o x 11 0.6249 Use a calculator to find tan 32o x 17.6 Simplify

#### Table Of Tangents And Cotangents

Example 3 Calculating Height Using the LAMPPOST tangent, find the height h of the street lamp to the nearest inch. tan 70o = opp. adj. Write the ratio of the tangent at 70o. tan 70o h = 40 substitutions. Multiply each side by 40. 40 tan 70o = h Use a calculator to simplify. 109.9 h Answer The lantern is about 110 inches tall.

7 Example 4 Use a special right triangle to find the tangent Use a special right triangle to find the tangent of a 60o angle. Step 1 Since all 30o-60o-90o triangles are similar, you can simplify the calculations by choosing 1 as the length of the shortest leg. Use the 30o-60o-90o triangle theorem to determine the length of the long leg.

Example 4 Use a special right triangle long leg = short leg 3 30o- 60o- 90o triangle theorem to find tangent x = 1 3 Substitute. x = 3 Simplify.

#### Find The Tangent Of The Angle Between The Lines Which Have Intercepts 3, 4, And 1, 8 On The X And Y Axes Respectively

Example 4 Use a special right triangle to find the tangent. STEP 2 Find tan 60o tan 60o = opp. adj. Write the ratio of the tangent of 60o. tan 60o = 3 1 Substitute. tan 60o = 3 Simplify. Answer The tangent of any 60o angle is 3 1.7321

Guided Practice For Examples 2, 3, and 4, find the value of x. Round to the nearest tenth. Answer 12.2 Answer 19.3 What if? In Example 4, assume that the side length of the short leg is 5 instead of 1. Show that the tangent at 60° is still equal to 5.

11 Daily Homework Quiz Use this chart for exercises 1-4. 1. If a = 18, b = 80, and c = 82, find tan B and tan A. Write each answer as a fraction and round to 4 decimal places. Answer tan B = 40 9 = ; tan A = =

### In The Diagram, Ab And Ac Are Tangents To A Circle, Center O And Radius 3.6cm. Calculate The Area Of The Shaded Region, Given That $\\left| \\!{\\underline {\\,{boc} \\,}} \\right. = \\dfrac{{2\\pi }}{

Daily Homework Quiz Use this chart for exercises 1-4. 2. If a = 17 and m A = 31, find b to the nearest tenth. o Answer 28.3

Daily Homework Quiz Use this chart for exercises 1-4. 3. If a = 9 and m B = 74, find b to the nearest tenth. o Answer 31.4

Daily Homework Quiz Use this chart for exercises 1-4. 4. If a = 5 and m B = 79, find the number of square units in the area of ABC to the nearest tenth. o Answer 64.3

#### Tangent Formula: Tangent Functions, Formulas, Solved Examples

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I have two circles labeled $A$ and $B$. Each of these circles has known positions $vec$ and $vec$ with radii $r_A$ and $r_B$ . I need to find the blue lines radiating from the origin of the circles at the angle ($theta_A$ or $theta_B$) shown in the diagram. These theta angles correspond to the angle from the origin of the circles to the point where the tangent line intersects the circle. The tangent must follow the diagram shown above so that $theta_A = theta_B + 180$. It must also be assumed that these circles never intersect $d = lVert vec – vec rVert > r_A + r_B$.

Enlarge the circle $A$ to the radius of $r_A+r_B$ while shrinking $B$ to $0$ . The common tangent maintains the same direction. Then you have a right triangle with sides $P_AP_B$ and $r_A+r_B$. You have now added the direction angle and triangle angle of $P_AP_B$.

#### The Tangent Ratio

Let us call the intersection of the line between the centers with a common tangent $O$. Then you will get two similar right triangles. $$|costheta_A|=frac-vec||}=|costheta_B|=frac-vec||}$$ you can also write $$||vec- vec|| +||vec-vec||=||vec-vec||=d$$ From here $$|costheta_A|=|costheta_B|= frac$ $d>r_A+r_B From $ you get $|costheta_A|<1$

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### Examples Find The Sine, Cosine And Tangent Of Angles A, B.

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#### If The Angle Between Two Tangents Drawn From An External Point ‘p’ To

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#### Tangents & Normals

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#### Angle Inclination Of A Line

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