I believe the answer would be 36.
Hope this helped you. ;}
I would say the answer is 5, please let me know if it’s right!
In this question, it is given that An inverse trigonometric function is used to find the value of an unknown obtuse angle in a triangle. The inverse function returns the angle 68°.
Since the angle is obtuse angle, it means the measurement of the angle is greater then 90 degree. And to find the angle measurement, we have to subtract the given angle from 180 degree.
So the unknown angle is
And that's the required answer .
a = 6, is your answer.
Square both sides
<span><span><span>9=a−2<span>(6−a)(2a−3)</span>+3</span>9=a-2\sqrt{(6-a)(2a-3)}+3</span><span>9=a−2<span>√<span><span><span>(6−a)(2a−3)</span></span><span></span></span></span>+3
</span></span>2 .Separate terms with roots from terms without roots
<span><span><span>9−a−3=−2<span>(6−a)(2a−3)</span></span>9-a-3=-2\sqrt{(6-a)(2a-3)}</span><span>9−a−3=−2<span>√<span><span><span>(6−a)(2a−3)
</span></span><span></span></span></span></span></span>
3. Simplify <span><span><span>9−a−3</span>9-a-3</span><span>9−a−3</span></span> to <span><span><span>6−a</span>6-a</span><span>6−a
</span></span><span><span><span>6−a=−2<span>(6−a)(2a−3)</span></span>6-a=-2\sqrt{(6-a)(2a-3)}</span><span>6−a=−2<span>√<span><span><span>(6−a)(2a−3)
</span></span><span></span></span></span></span></span>
4 .Square both sides
<span><span><span><span><span>(6−a)</span>2</span>=4(6−a)(2a−3)</span>{(6-a)}^{2}=4(6-a)(2a-3)</span><span><span><span>(6−a)</span><span><span>2</span><span></span></span></span>=4(6−a)(2a−3)
</span></span>5 .Expand
<span><span><span>36−12a+<span>a2</span>=48a−72−8<span>a2</span>+12a</span>36-12a+{a}^{2}=48a-72-8{a}^{2}+12a</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>=48a−72−8<span>a<span><span>2</span><span></span></span></span>+12a
</span></span>6. Simplify <span><span><span>48a−72−8<span>a2</span>+12a</span>48a-72-8{a}^{2}+12a</span><span>48a−72−8<span>a<span><span>2</span><span></span></span></span>+12a</span></span> to <span><span><span>60a−72−8<span>a2</span></span>60a-72-8{a}^{2}</span><span>60a−72−8<span>a<span><span>2</span><span></span></span></span></span></span>
<span><span><span>36−12a+<span>a2</span>=60a−72−8<span>a2</span></span>36-12a+{a}^{2}=60a-72-8{a}^{2}</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>=60a−72−8<span>a<span><span>2
</span><span></span></span></span></span></span>
7. Move all terms to one side
<span><span><span>36−12a+<span>a2</span>−60a+72+8<span>a2</span>=0</span>36-12a+{a}^{2}-60a+72+8{a}^{2}=0</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>−60a+72+8<span>a<span><span>2</span><span></span></span></span>=0
</span></span>8. Simplify <span><span><span>36−12a+<span>a2</span>−60a+72+8<span>a2</span></span>36-12a+{a}^{2}-60a+72+8{a}^{2}</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>−60a+72+8<span>a<span><span>2</span><span></span></span></span></span></span> to <span><span><span>36−72a+9<span>a2</span>+72</span>36-72a+9{a}^{2}+72</span><span>36−72a+9<span>a<span><span>2</span><span></span></span></span>+72</span></span>
<span><span><span>36−72a+9<span>a2</span>+72=0</span>36-72a+9{a}^{2}+72=0</span><span>36−72a+9<span>a<span><span>2</span><span></span></span></span>+72=0
</span></span>9 .Simplify <span><span><span>36−72a+9<span>a2</span>+72</span>36-72a+9{a}^{2}+72</span><span>36−72a+9<span>a<span><span>2</span><span></span></span></span>+72</span></span> to <span><span><span>−72a+9<span>a2</span>+108</span>-72a+9{a}^{2}+108</span><span>−72a+9<span>a<span><span>2</span><span></span></span></span>+108</span></span>
<span><span><span>−72a+9<span>a2</span>+108=0</span>-72a+9{a}^{2}+108=0</span><span>−72a+9<span>a<span><span>2</span><span></span></span></span>+108=0
</span></span>10.Factor out the common term <span><span>99</span>9</span>
<span><span><span>−9(8a−<span>a2</span>−12)=0</span>-9(8a-{a}^{2}-12)=0</span><span>−9(8a−<span>a<span><span>2</span><span></span></span></span>−12)=0
</span></span>11. Factor out the negative sign
<span><span><span>−9×−(<span>a2</span>−8a+12)=0</span>-9\times -({a}^{2}-8a+12)=0</span><span>−9×−(<span>a<span><span>2</span><span></span></span></span>−8a+12)=0
</span></span>12. Divide both sides by <span><span><span>−9</span>-9</span><span>−9</span></span>
<span><span><span>−<span>a2</span>+8a−12=0</span>-{a}^{2}+8a-12=0</span><span>−<span>a<span><span>2</span><span></span></span></span>+8a−12=0
</span></span>13. Multiply both sides by <span><span><span>−1</span>-1</span><span>−1</span></span>
<span><span><span><span>a2</span>−8a+12=0</span>{a}^{2}-8a+12=0</span><span><span>a<span><span>2</span><span></span></span></span>−8a+12=0
</span></span>14. Factor <span><span><span><span>a2</span>−8a+12</span>{a}^{2}-8a+12</span><span><span>a<span><span>2</span><span></span></span></span>−8a+12</span></span>
<span><span><span>(a−6)(a−2)=0</span>(a-6)(a-2)=0</span><span>(a−6)(a−2)=0
</span></span>15. Solve for <span><span>aa</span>a</span>
<span><span><span>a=6,2</span>a=6,2</span><span>a=6,2
</span></span>16 Check solution
When <span><span><span>a=2</span>a=2</span><span>a=2</span></span>, the original equation <span><span><span>−3=<span>6−a</span>−<span>2a−3</span></span>-3=\sqrt{6-a}-\sqrt{2a-3}</span><span>−3=<span>√<span><span><span>6−a</span></span><span></span></span></span>−<span>√<span><span><span>2a−3</span></span><span></span></span></span></span></span> does not hold true.
We will drop <span><span><span>a=2</span>a=2</span><span>a=2</span></span> from the solution set.
17. Therefore,
<span><span><span>a=6</span></span><span /></span>
