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Question In Delta XYZ,x=410inches,y=450inches and z=210inches Find the measure of angle X to the nearest degree. Answer Attemptiout of square

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Question In Delta XYZ,x=410inches,y=450inches and z=210inches Find the measure of angle X to the nearest degree. Answer Attemptiout of square

Question In Delta XYZ,x=410inches,y=450inches and z=210inches Find the measure of angle X to the nearest degree. Answer Attemptiout of square

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BlakeMaster · Tutor for 5 years

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### $65^\circ$

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## Step 1: Identify the law to use<br />### To find the measure of an angle in a triangle when all three sides are known, we use the Law of Cosines.<br />## Step 2: Apply the Law of Cosines<br />### The Law of Cosines states: $c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$. Here, we need to find $\angle X$, so we rearrange the formula to solve for $\cos(X)$.<br />## Step 3: Substitute the given values<br />### Substitute $x = 410$, $y = 450$, and $z = 210$ into the formula: <br />\[ \cos(X) = \frac{y^2 + z^2 - x^2}{2yz} \]<br />\[ \cos(X) = \frac{450^2 + 210^2 - 410^2}{2 \cdot 450 \cdot 210} \]<br />## Step 4: Calculate the cosine value<br />### Compute the values:<br />\[ \cos(X) = \frac{202500 + 44100 - 168100}{189000} \]<br />\[ \cos(X) = \frac{78500}{189000} \]<br />\[ \cos(X) \approx 0.4153 \]<br />## Step 5: Find the angle using the inverse cosine function<br />### Use the inverse cosine function to find $\angle X$:<br />\[ X = \cos^{-1}(0.4153) \]<br />\[ X \approx 65.4^\circ \]<br />## Step 6: Round to the nearest degree<br />### Round $65.4^\circ$ to the nearest degree:<br />\[ X \approx 65^\circ \]
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