A homeowner drew a sketch of their triangle - shaped garden as shown above. Although the sketch was not drawn accurately to scale, the triangle was labelled with the proper dimensions. What is the value of `sinx`?

If the area of the triangle shown above is 12 squares inches, what is the value of cosz?

Two isosceles triangle are shown above. If 180-z=2y and y=75, what is the value of x?

In the figure shown above, ABC is a triangle right angled at B. What is the value of angle A, in degrees?

A transparent cube of glass of refractive index mu and thickness t is placed on a spot of ink drawn on a white paper, When the spot is viewed from above (air) normally, the spot appears to shift through a distance of Delta t towards the observer. What is the value of Delta t ?

Two moles of a perfect gas undergo the following process: (a) A reversible isobaric expansion from ( 1.0 atm, 20.0 litre) to ( 1.0 atm, 40.0 litre). (b) A reversible isochoric change of state from ( 1.0 atm, 40.0 litre) to ( 1.0 atm, 40.0 litre). (b) A reversible isochoric change of state from ( 1.0 atm, 40.0 litre) to ( 0.5 atm, 40.0 litre). (c) A reversible isothermal compression from ( 0.5 atm, 40.0 litre) to ( 1.0 atm, 20.0 litre). (i) Sketch with labels each of the process on the same P-V diagram. (ii) Calculate the total work (W) and the total heat change (q) involved in the above process. (iii) What will be the value of DeltaU, DeltaH and DeltaS for the overall process?

Sushant prepared a problem. Construct /_\ XYZ in which XY =2 cm , YZ = 8 cm and XZ = 4 cm. He also drew the rough sketch as shown is figure (i).Reading the problem, Srija told Sushant that it would not be possible to draw the triangle with the given measurements. However, Sushant started to draw the diagram as shown in figure (ii). Check whether Sushant can draw the triangle. If not why? Discuss with your friends. What property of triangles supports Srija's idea?

In triangle RST above, point W (not shown) lies on bar(RT) . What is the value of cos( angleRSW) − sin(angleWST) ?