Exercises
Put your right triangle skills to the test! This quiz covers key geometry and trigonometry concepts used to solve right triangles, including complementary acute angles, sine and tangent ratios, hypotenuse calculations, and finding opposite sides. Practice applying trigonometric relationships to triangles with given angles and side lengths, such as 30°, 45°, and 60° special-angle situations. Whether you are reviewing for a math class or strengthening your understanding of basic trigonometry, these questions will help you check your ability to identify the correct ratio and solve efficiently.
Answer the questions below and check the explanation for each answer.
0/5 answered
Auto audio on: the next questions will be read aloud when you click Continue.
In a right triangle, the sum of the two acute angles must be 90 degrees because the third angle measures 90 degrees by definition. If one acute angle is 35 degrees, the other acute angle must be 90 - 35 = 55 degrees. Thus, the correct option is 1.
In a right triangle with an angle of 30 degrees, the side opposite the angle is half the hypotenuse. Here, the given leg is adjacent, not hypotenuse or opposite, so the adjacent side relates to the hypotenuse using cosine: cos(30) = adjacent/hypotenuse. Thus, cos(30)=7/hypotenuse leads to 7/(√3/2) = hypotenuse, which simplifies to 14 units.
The sine of 45 degrees is known to be 1/√2. This is because in a 45-degree angle of a right-angled triangle, the opposite and adjacent sides are equal, forming a 1:1 ratio, and the hypotenuse is √2, resulting in a sine value of 1/√2.
In a right triangle, the side opposite to a 60-degree angle can be found using the sine function. Sine of 60 degrees is √3/2. With a hypotenuse of 10 units, the length of the opposite side is 10 * (√3/2) = 5√3 units. Therefore, the correct option is 3.
In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. For the angle opposite the 8-unit side, the opposite side is 8 units and the adjacent side is 15 units. Therefore, the tangent of the angle is the ratio of the opposite side (8 units) to the adjacent side (15 units), which is 8/15.
Free CourseTrigonometry Grade 11
5
(1)
4h29m
39 exercises
Free CourseTrigonometry
4.6
(40)
6h35m
39 exercises
Free CourseTrigonometry
4.6
(17)
9h25m
32 exercises
Free CourseTrigonometry for beginners
4
(2)
45m
5 exercises
Free CourseTrigonometry full course
New
9h48m
6 exercises
Free CourseTrigonometry
New
16h32m
38 exercises
Free CourseTrigonometry Course
New
6h14m
52 exercises
Thousands of online courses in video, ebooks and audiobooks.
To test your knowledge during online courses
Generated directly from your cell phone's photo gallery and sent to your email
Download our app via QR Code or the links below:.
Carry knowledge in your pocket.
Download the Cursa app.
There are hundreds of free courses available, with a free certificate of completion that is saved in your mobile image gallery.
Download the app to access the Course Completion Certificate for Free.
+ 10 million
students
Free and Valid
Certificate
60 thousand free
exercises
4.8/5 rating in
app stores
Free courses in
video and ebooks