Questions: Solve the following problems. C) Given: triangle AKM inscribed in k(O, r=2), m angle A=33°, and O in AM Find: Perimeter of triangle AKM

Solve the following problems. C) Given: triangle AKM inscribed in k(O, r=2), m angle A=33°, and O in AM Find: Perimeter of triangle AKM
Transcript text: Solve the following problems. C) Given: $\triangle \mathrm{AKM}$ inscribed in $k(\mathrm{O}, r=2), \mathrm{m} \angle \mathrm{A}=33^{\circ}$, and $\mathrm{O} \in$ AM Find: Perimeter of $\triangle A K M$ Answer: $P_{A K M} \approx$ $\square$ units
failed

Solution

failed
failed

Solution Steps

Step 1: Find the measure of arc KM

Since OE $\perp$ AM, AM is a chord and OE is a radius. The perpendicular from the center of a circle to a chord bisects the chord and its arc. Therefore, arc AE $\cong$ arc ME. Arc AM = 2 * $\angle$ A = 2 * 33° = 66°.

Step 2: Find the measure of arc AK

Since AAKM is inscribed in circle O, we know that the sum of the arcs intercepted by inscribed angles A and M is 180°. Arc KM + arc AK = 180°, so arc KM = $\angle$ 2A = 2 * 33° = 66°. Because arc KM = 66°, then arc AK = 180° - 66° = 114°.

Step 3: Find the length of chord AK

The length of a chord is given by the formula 2r * sin($\frac{c}{2}$) where $c$ is the central angle that subtends the chord. In this case, $c$ = 114° and $r$ = 2. Therefore AK = 2 * 2 * sin($\frac{114}{2}$) = 4 * sin(57°). AK $\approx$ 3.35

Step 4: Find AM

AM = 2 * AO * cos(A) AM = 2 * 2 * cos(33°) AM $\approx$ 3.35

Step 5: Find KM

Using the Law of Cosines where a, b, and c are sides of a triangle and angle C is opposite side c: $c^2 = a^2 + b^2 - 2ab$ cos(C) $KM^2 = AK^2 + AM^2 - 2(AK)(AM)$ cos(A) $KM^2 = 3.35^2 + 3.35^2 - 2(3.35)(3.35)$ cos(33°) $KM \approx$ 1.91

Final Answer: The perimeter of $\triangle$AKM is AK + KM + AM $\approx$ 3.35 + 3.35 + 1.91 $\approx$ 8.61 units.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Dice Rolls: You roll a pair of fair 6 -sided dice. Use the information below to answer the questions. a) First let's complete the sample space. The sample space is the set of all possible outcomes from a probability experiment. Therefore, we want to list all the outcomes if you roll a pair of fair 6 -sided dice. If you roll a 2 on the first die and a 4 on the second die then the entry will be 2,4. Fill in the blanks following this pattern (Hint: do not put any spaces in the blanks). 2nd roll=1 2nd roll=2 2nd roll=3 2nd roll=4 2nd roll=5 2nd roll=6 1st roll=1 1,1 1,2 1,3 1,4 1,5 1,6 1st roll=2 2,1 2,2 2,4 2,5 2,6 1st roll=3 3,2 3,3 3,4 3,5 3,6 1st roll=4 4,1 4,2 4,4 4,5 4,6 1st roll=5 5,1 5,2 5,3 5,4 5,5 5,6 1st roll=6 6,1 6,3 6,4 6,5 b) When you roll both dice and add up the pips (pips are the dots on the dice), what's the probability of getting a sum of 1 ? (round to 4 decimal places, if necessary) c) When you roll both dice and add up the pips, what's the probability of getting a sum of 5 ? (round to 4 decimal places, if necessary) d) When you roll both dice and add up the pips, what's the probability of getting a sum of 12? (round to 4 decimal places, if necessary)
failedAnswered
Solve the logarithmic equation. Express all solutions in exact form. log4(x^3+8) = 2 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is . (Simplify your answer. Use a comma to separate answers as needed.) B. The solution is the empty set.
failedAnswered
Question 6 (2.5 points) What are the simplest types of eukaryotes? plants protists fungi bacteria archaea
failedAnswered
Which of the following are the suggested methods to deal with bullying? (Choose every correct answer.) Document bullying behaviors. Do not strike back. Get others on your side. Identify places to hide. Seek revenge.
failedAnswered
이차함수 (y=x^2+2 x+5) 의 최솟값은?