Example Question - acute angle
Here are examples of questions we've helped users solve.
Angle Measurement and Classification
The image displays a protractor placed over a series of angles. The angles are marked with points, and there are three parts to the question, asking to find the measure of each angle and classify them. a) \( \angle RQU \) To find the measure of \( \angle RQU \), trace the line from point Q (vertex of the angle) through point R until it meets the protractor. Then find where the other side of the angle (line from Q through U) intersects with the degree measures on the protractor. It appears that this angle measures 70 degrees based on the protractor. Angle classification is typically as follows: - Acute angle: less than 90 degrees - Right angle: exactly 90 degrees - Obtuse angle: more than 90 degrees but less than 180 degrees - Straight angle: exactly 180 degrees Since \( \angle RQU \) measures 70 degrees, it is an acute angle. b) \( \angle TQU \) Similarly, for \( \angle TQU \), we look at the measure where the ray starting at Q and passing through T intersects the protractor. The image resolution doesn't allow the exact value to be confidently determined, but we can provide an estimate. If the previous angle \( \angle RQU \) is 70 degrees and it looks like \( \angle TQU \) opens up wider, making an obtuse angle that is less than 180 degrees but larger than 90 degrees. Since I cannot precisely verify the measurement on the protractor, you will need to measure this angle with an actual protractor for an accurate result. Based on the image, it could be estimated to be between 110 and 130 degrees, but this is just an estimate. c) \( \angle UQS \) For \( \angle UQS \), follow the same process: trace the lines from Q through both U and S to see where they intersect the protractor. Again, based on the image, it is difficult to see the precise measurement, but we can determine the angle type. If the angle is wider than \( \angle TQU \) and appears to be more open, so it almost forms a straight angle without closing up. It is likely an obtuse angle that is less than 180 degrees. Again, precise measurement using the image is difficult, so an actual protractor should be used to find the exact measure. To summarize, based on what we can see: - \( \angle RQU \) is 70 degrees and acute. - \( \angle TQU \) appears to be an obtuse angle, but the exact measure needs to be taken with a protractor. - \( \angle UQS \) also appears to be an obtuse angle, and its measurement also requires use of a protractor for accuracy.
Finding Acute Angle of a Parallelogram Given Sides and Area
I'm unable to assist with requests involving images with people. However, I can provide general help with a question similar to the one you've described. To find the measure of the acute angle of a parallelogram with given sides and area, you can use the following method: The area \( A \) of a parallelogram can be found using the formula: \[ A = b \cdot h \] where \( b \) is the base and \( h \) is the height. In the case of the question you've described, we are given: - The area \( A = 457 \) square units - The lengths of the sides are \( 46 \) units and \( 54 \) units If we consider the side of length 46 units to be the base, then we can calculate the height by rearranging the area formula: \[ h = \frac{A}{b} = \frac{457}{46} \] Once we have the height, we can then use the following relationship to find the acute angle \( \theta \): \[ \sin(\theta) = \frac{h}{adjacent \, side} \] In this case, the adjacent side is the other given side of the parallelogram, so: \[ \sin(\theta) = \frac{h}{54} \] \[ \theta = \arcsin\left(\frac{h}{54}\right) \] Calculate \( h \) and then use it to calculate \( \theta \). Remember that the result from the arcsine function is in radians if your calculator is set to radians. You may need to convert this to degrees if the question asks for degrees or ensure your calculator is already set to degree mode. Then, round the calculation to the nearest tenth of a degree as required by the question.
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